Product Description

Enables the reader to develop general principles from which equations of motions may be derived

Stresses the importance of symmetries as a basis for quantum mechanics and to get practice in using theoretical tools and concepts that are essential for all branches of physics.

The book contains numerous problems with complete solutions, and some practical examples.

Students appreciate the thoroughness and clarity of this book.

Customer Reviews (1)

Fast paced but clearly written
For the listed price of $38US this book is indeed a bargain.It is clearly written with a rational organization of topics and most sections are accompanied with meaningful examples.I especially enjoyed the development of the Hamiltonian.On the other hand, this is not an easy text - you may not be able to watch Jerry Springer as you read it; a basic familiarity calculus, vector analysis and physics will be needed to make any head way at all.I wish I had used this text in college. ... Read more

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One of the first books in this area, this text focuses on important aspects of the system operation, analysis and performance evaluation of selected chaos-based digital communications systems – a hot topic in communications and signal processing.

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Simple and mechanical systems are the fouundation of Science: a particle sliding on a two-dimensional surface in mathematics, the solar system in astronomy, the hydrogen and the helium atoms in physics, and small molecules in chemistry. Although elementary and deterministic, their motions look almost random over long time intervals, and cannot be explained by the traditional approaches. This book describes the apparent chaos in these systems for an audience at the level of beginning graduate students, developing the relevant ideas of the last two decades with the help of geometric intutition rather than algebraic manipulation. The main focus is on seeking the connection between classical and quantum mechanics: classical chaos is rough and fractal, whereas quantum chaos is smooth and elusive; and yet the former should be the limit of the latter as Planck's quantum becomes small. The historical and cultural background is mentioned, and the text discusses realistic examples in some detail thereby providing readers a new perspective and preparing them to tackle new problems in this rich field. ... Read more

Customer Reviews (8)

A good start - but you will need more
Gutzwiller is the master and one of the main contributors of quantum chaos. His writing is expansive and insightful. However this books doesn't serve as a textbook by its own, as it is overly concise, short of mathematical rigor and overlooking a lot of aspects in the classical chaos (which I think is fair).

Chatty and fun, but not to be used as the basis for anything but a reading course
There are all kinds of physics books. There are books for didactics; nobody actually uses, say, Jackson's book on Classical Electrodynamics for anything but didactics. You can tell the books that are useful for teaching in a classroom by the presence of extensive problem sets. This book has none. So, with this, let me dispose of the notion that you should be able to teach a 'quantum chaos' course based on this book. There are also books which explain in great technical detail all about a given small subject area; Fritz Haake's book on 'Quantum Signatures of Chaos' is a good example of this (though it's really about Random Matrix theory, which is but one quantum signature of chaos; a whole book on just one small area of this subject -covered in a few pages in Gutzwiller's book). Then there are books which are reviews of a subject. Gutzwiller wrote a book which is a review of a subject. It's a very good one.

One could actually go through this, read it, know about the existence of many things, and read up on them as is appropriate for one's research. That is how I used the book. Gutzwiller writes very well, and communicates his enthusiasm for the subject matter. The bibliography is extensive, and you could indeed learn all about anything you needed to by going through the bibliographic references for the details. An actual review which takes you from knowing about Hamilton Jacobi theory and the WKB approximation and covering all the material he presented in every detail needed to understand the whole mess .... I doubt as any such book exists. It would be an encyclopedia. If you simply want to understand the Gutzwiller trace formula starting at that level, there are books which do it reasonably well (Cvitanovic's is a great effort in that direction). This is not such a book; this is a review. A review of a very important body of work. That is this book's purpose, and it serves it admirably well.

As for why Gutzwiller is important; if you think the correspondence principle is interesting, the Gutzwiller trace formula is the main useful way we know of thinking about it in detail. Most physicists think about the area where quantum mechanics becomes classical as a sort of intellectual blur. This is a mistake. This is arguably a much more interesting place to think about than, say, what happened in the first 10^-35 seconds of the big bang. For example, one can actually do experiments in the semiclassical regime. Experiments which only involve optics. There's gold in them there hills, and nobody is looking there. Mesoscopic physics as applied to device physics may eventually force people to think about these issues in detail, but I somehow doubt the device guys are going to reinvent quantum mechanics. Gutzwiller thought about these issues in the 1960s while working on practical problems for IBM. These are thefundamental mysteries, folks: if you're an ambitious young physicist who wants to make a real contribution to science; leave the noodle theory alone, and look into this stuff. Following the herd will get you a nice career, but immortality belongs to the one who plays Einstein or Poincare to Gutzwiller's Minkowski.

Close to Useless
I am used to reading graduate texts where I have to fill in extensive portions of the logic.However, this book does not even begin to explain the results contained in it.It is simply a collection of results, with references to other texts with little explanation (although he does a good job motivating the results).

As I was writing this review, I opened the book to a random page (279) and found the following: "Zaslavski (1977) also starts from the trace formula; he gets a rather explicit expression for the spacing probability P(x) which involves the Kolmogorov entropy..."How did he do this?Well, if you want to know then you have to go read Zaslavski to find out.The entire book is this way.

Maybe this is a great reference for the researcher who already understands the field, but for someone trying to learn it from this book it's worthless.

We need more books on the subject
While the question of connecting quantum theory to classical
mechanics, ODEs, PDEs, etc is a very deep one, and the
author is a main contributor in the subject, the books
lacks of narrative momentum... Readers of, say, QFT a la
Itzkinson-Zuber will be accostumed to this, but I feel a
more focused work on the subject is still to be written.

The Father of the Quasiclassical Approach to Quantum Chaos
Today the Gutzwiller trace formula is the standard quasiclassical approach to studies of the spectrum in quantum chaos research.
The most striking property of classics chaos is the sensitive dependence on initial conditions such that neighboring trajectories in phase space separate at an exponential rate. As result the long time behavior of the system is unpredictable. Instead of looking for exponential sensitivity, the main stream of quantum chaos research is currently concentrated on identifying the fingerprints of classical chaos in quantum systems. If one were to identify unique fingerprints of classical chaos in quantum mechanics, one could use these to define quantum chaos.
The starting point for the Gutzwiller quasiclassical analysis is the path integral formulation of the propagator. From this quantum expression one can deduce a formula that contains a sum over all classical periodic orbits. This is the main contribution of Gutzwiller.
Excellent Book! ... Read more

Product Description
The Second Woodward Conference, held November 17-18, 1989 at San Jose State University, brought together pioneers and experts from a number of different disciplines to discuss problems involving nonlinear structures in physical systems, with emphasis on pattern formation, chaos and waves. These proceedings contain results of interest to workers in physics, chemistry, biology, materials science and mathematics. Topics discussed include: - pattern formation of bubbles, viscous fingers, electrodeposits, solidifications, chemical systems and frustrated systems - chaos, self-organized criticality and complex systems - convection and traveling waves in simple and com- plex liquids - nonlinear structures in materials such as magnetic systems, polymers, fluid dispersions, and glassy and solid thin films - other nonlinear structures in plasmas, premixed flames, biological systems etc. ... Read more

Product Description
The book is about new applications of cellular neural networks (CNNs), new theoretical results and implementation issues. This topic involves several scientific disciplines including circuit theory, microelectronics, dynamic systems theory and applied mathematics, information processing, biology, neurophysiology, and robotics, to cite but a few. Significant attention is paid to small-size CNNs for generating chaotic dynamics and also to their application in the area of nonlinear circuit synchronization and secure communication. Complex spatio-temporal phenomena in simple CNN models are investigated. A CMOS discrete-time switched-current implementation of a CNN is presented in detail. The reader will find thorough discussion on the subject, ranging from the highest-level aspects treated in a rigorous and analytic way, to the technological challenges and the circuit design aspects. ... Read more

Customer Reviews (2)

A very good work!
Don't you know Cellular Neural Networks? Read this book, even if you are not a specialist. I like it a lot, it's very interesting. I had a course project on CNN for my master in electronic engineering but I never found aso clear book in describing principles, applications and circuitrealizations about CNN. Don't be scared if you can find some high leveltheoretical contents, they are for specialist in that field only, but theyare not necessary for novices to know of CNN. Excellent!

this is excellent! Even for novices!
I definitely enjoyed reading this book. I found it extremely clear and interesting. I am an electrical engineer but I am certainly not a specialist of this field. However, I catched up with the subject veryquickly. And it is amazing to see how many applications these CNN have. Asa matter of fact some of the discrete component circuits here described caneven be realized by an electronics hobbyst like me. And I plan to do my ownexperiments. I admit I wasn't able to follow some parts with high leveltheoretical contents (some math definitely goes beyond my understanding).Nevertheless I found it very appealing. In summary I would encourage eventhe novices to check it out. I like it a lot. ... Read more

Product Description

This volume contains papers written by the invited lecturers and the contributors (short reports and posters). The papers do not necessarily cover exactly one-to-one what has been presented at the conference - for that we would need at least one thousand pages - but contains the material related to the presentations, either in the sense of a review (20%) or in the sense of a new original contribution (80%). The volume is a valuable source of scientific information in the general field of nonlinear science in its broadest sense, namely in the fundamental and applied physics, and in the interdisciplinary physics.

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Chaos control refers to purposefully manipulating chaotic dynamical behaviors of some complex nonlinear systems. There exists no similar control theory-oriented book available in the market that is devoted to the subject of chaos control, written by control engineers for control engineers. World-renowned leading experts in the field provide their state-of-the-art survey about the extensive research that has been done over the last few years in this subject. The new technology of chaos control has major impact on novel engineering applications such as telecommunications, power systems, liquid mixing, internet technology, high-performance circuits and devices, biological systems modeling like the brain and the heart, and decision making. The book is not only aimed at active researchers in the field of chaos control involving control and systems engineers, theoretical and experimental physicists, and applied mathematicians, but also at a general audience in related fields. ... Read more

Product Description

Electronics, optics, and fluids have been strong fields for the application of nonlineardynamics. The trend over the years has been the growth of biophysics (especially neuroscience and cardiac dynamics), oceanography, and geophysics for the employment of the concepts and techniques of nonlinear dynamics. Topics include: electronics; optics; geophysics, oceanography, and meterology; hydrodynamics, turbulence, and plasmas; biophysics; neurophysiology; chemical chaos; interdisciplinary; as well as data analysis.

Product Description
The Session was intended to give a broad survey of the mathematical problems arising in the chaotic transition of deterministic dynamical systems, both in classical and quantum mechanics.
The lectures of Mather and Forni thoroughly cover the area- preserving twist maps, and include an up-to-date version of the Aubry-Mather theory.
The lectures of Bellissard describe the quantum aspects: classical limit, localization, spectral properties of the relevant Schrödinger operators and thus represent an exhaus- tive introduction to the mathematics of "quantum chaos".
The lectures of Degli Esposti et al. reviews equidistribu- tion of unstable periodic orbits and classical limit of quantized toral symplectomorphisms. ... Read more

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This updated and revised fourth edition covers all topics in mechanics from elementary Newtonian mechanics, canonical and rigid body mechanics to relativistic mechanics and nonlinear dynamics.

Customer Reviews (3)

A very complete book
Although I agree that one might be scared by the presence of sophisticated chapters like the one devoted to differential geometry, I find that this book is the best for an undergraduate level. It begins with Newtonian mechanics (some knowledge on linear algebra and calculus assumed) and covers all the fundamental points of modern mechanics in a rigorous and straightforward way, including a chapter in special relativity and another on dynamical systems and chaos. As it emphasizes the relevant role of symmetries, it naturally leads to quantum mechanics and can be used by advanced undergrad or graduate students interested in the geometrical foundations of mechanics.
Even though it is certainly not the easiest book available, if you have to buy just one, buy this!

Excellent, but not as a first contact with Mechanics
I would agree on the rather high quality of the present
book, as pointed out in the other review.

However, the books seems not appropriate for a first contact
with Newtonian mechanics.

While the book makes every effort to introduce the reader to
modern concepts used in Mechanics, notably its setting in a
differential geometric context and an introduction to nonlinear
dynamical systems, the very basis of vector mechanics receives
only attention from one chapter.

This is clearly inadequate and a thourough understanding of
elementary vector mechanics and a good round of problem solving
is certainly essential before addressing even the simplest
Lagrangian mechanics.

The reason I want to point this out, is that the book is used
at an early level in German universities.

That is scary. I can well imagine people attempting to walk
through tangent spaces, but not able to integrate a simple
dynamics problem in R^2.

Please be careful!

The greatest undergratuate book in Mechanics.
This book is the greatest there is for a study of mechanics on an undergratuate level. This book covers alot of subjects with a unique combination of strictness and easyness. It's a must for all physics andmathematics students. It's index: 1.Elementary Newton Mechanics 2.ThePrinciples of Canonical Mechanics 3.The Mechanics of Rigid Bodies4.Relativistic Mechanics 5.Geometric Apsects of Mechanics 6.Stability andChaos 7.Continuous Systems ... Read more

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The articles treat subjects such as the social responsibility of scientists, thermonuclear processes in stars and stellar neutrinos, turbulence and the emergence of planetary systems.

Considerable attention is paid to the unity of nature, the nature of time, and to information about, and interpretation of, the structure of quantum theory, all important philosophical problems of our times.

The last section describes von Weizsäcker's ur-hypothesis and how it will theoretically permit the construction of particles and interactions from quantized bits of information.

Product Description

This book explores non-extensive statistical mechanics in non-equilibrium thermodynamics, and presents an overview of the strong nonlinearity of chaos and complexity in natural systems, drawing on relevant mathematics from topology, measure-theory, inverse and ill-posed problems, set-valued analysis, and nonlinear functional analysis. It offers a self-contained theory of complexity and complex systems as the steady state of non-equilibrium systems, denoting a homeostatic dynamic equilibrium between stabilizing order and destabilizing disorder.

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Written in Alwyn Scott’s inimitable style, one that readers will find both lucid and accessible, this masterwork elucidates the explosion of activity in nonlinear science in recent decades. The book explains the wide-ranging implications of nonlinear phenomena for future developments in many areas of modern science, including mathematics, physics, engineering, chemistry, biology, and neuroscience. Arguably as important as quantum theory, modern nonlinear science is essential for understanding the scientific developments of the twenty-first century.

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This proceedings volume contains foundation of anticipation in any system and applications in all the areas of science: economy, biology, cognition, physics, robotics, etc. Strong anticipatory systems deal with systems which behave in taking into account past, present and computed future states. The new mathematical and computational tools of incursion and hyperincursion are developed in this way. In weak anticipatory systems, the future states are predicted from models of these systems. The domain of computing anticipatory systems is becoming a new frontier of science. ... Read more

Customer Reviews (1)

A new kind of science...
I have read many of papers contained in the three CASYS conference proceedings and have been quite impressed with the direction anticipatory systems research is heading.Anticipatory systems research is derived from Robert Rosen's seminal works "Anticipatory Systems", "Life Itself" and "Essays on Life Itself"; these were basically ignored (much like Rashevsky's work prior to Rosen) but slowly its value is being realized.

Anticipatory systems acknowledge that real processes, particularly life, do not obey causal laws required by our present 'religion' of reductionism.This can be seen in all aspects of science whether one looks at attempts at cybernetics, algorithmic information theory, physics or biology (to name a few).We have consistently run up against the same roadblocks to progress since our present way of thinking excludes the possibility of ever answering some very basic questions.

There is a lot of interest here from Dubois' works in hyperinclusion (although I do not agree with his interpretation of Rosen) to Ekdahl's excellent research on the link between induction and anticipatory systems.Nadin's work is quite good for someone just beginning to get interested in this area.Many aspects of science that are complete mysteries now begin to make much more sense whether it is the Feynman-Wheeler theories of QED, understanding Shnoll's results or learning theories in general when one sees that the problem is our clinging to linear causality.

It is quite interesting to contrast this to Wolfram's pinnacle of ironic science, "A New Kind of Science" - he has no 'new' science, just more of the old stuff.Unfortunately his money has helped him generate lots of hype about fluff when there is much more exciting and genuinely new work being done as it has in the past:quietly and thoughtfully. ... Read more

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This book attempts to present some current research progress and results on the interplay of fuzzy logic and chaos theory. More specifically, this book includes a collections of some state-of-the-art surveys, tutorials, and application examples written by some experts working in the interdisciplinary fields overlapping fuzzy logic and chaos theory. The content of the book covers fuzzy definition of chaos, fuzzy modeling and control of chaotic systems using both Mamdani and Takagi-Sugeno models, fuzzy model identification using genetic algorithms and neural network schemes, bifurcation phenomena and self-referencing in fuzzy systems, complex fuzzy systems and their collective behaviours, as well as some applications of combining fuzzy logic and chaotic dynamics, such as fuzzy-chaos hybrid controllers for nonlinear dynamic systems, and fuzzy-model-based chaotic cryptosystems. This book can serve as a handy reference for researchers working in the interdisciplines related, among others, to both fuzzy logic and chaos theory. ... Read more

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This volume includes the results derived during last ten years about both suppression and synchronization of chaotic -continuous time- systems. Along this time, the concept was to study how the intrinsic properties of dynamical systems can be exploited to suppress and to synchronize the chaotic behaviour and what synchronization phenomena can be found under feedback interconnection. A compilation of these findings is described in this book. This book shows a perspective on synchronization of chaotic systems.

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Chaos: A Program Collection for the PC presents an outstanding selection of executable programs with introductory texts to chaos theory and its simulation. Students in physics, mathematics, and engineering will find a thorough introduction to fundamentals and applications in this field. Many numerical experiments and suggestions for further studies help the reader to become familiar with this fascinating topic. The second edition includes one CD-ROM, the executable programs are Windows 95 compatible. ... Read more

Product Description

This new edition strives yet again to provide readers with a working knowledge of chaos theory and dynamical systems through parallel introductory explanations in the book and interaction with carefully-selected programs supplied on the accompanying diskette. The programs enable readers, especially advanced-undergraduate students in physics, engineering, and math, to tackle relevant physical systems quickly on their PCs, without distraction from algorithmic details. For the third edition of Chaos: A Program Collection for the PC, each of the previous twelve programs is polished and rewritten in C++ (both Windows and Linux versions are included). A new program treats kicked systems, an important class of two-dimensional problems, which is introduced in Chapter 13. Each chapter follows the structure: theoretical background; numerical techniques; interaction with the program; computer experiments; real experiments and empirical evidence; reference. Interacting with the many numerical experiments have proven to help readers to become familiar with this fascinating topic and even to enjoy the experience.

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This book deals with collective and stochastic processes in astrophysical disks involving theory, observations, and the results of modelling. It examines the spiral-vortex structure in galactic and accretion disks, and stochastic and ordered structures in developed turbulence. The book advances the study in this important branch of astrophysics and will benefit professional researchers, lecturers, and graduate students.

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Fractal geometry is used to model complicated natural and technical phenomena in various disciplines like physics, biology, finance, and medicine. Since most convincing models contain an element of randomness, stochastics enters the area in a natural way. This book documents the establishment of fractal geometry as a substantial mathematical theory. As in the previous volumes, which appeared in 1998 and 2000, leading experts known for clear exposition were selected as authors. They survey their field of expertise, emphasizing recent developments and open problems. Main topics include multifractal measures, dynamical systems, stochastic processes and random fractals, harmonic analysis on fractals.