Download or read book Physics Of Chaos In Hamiltonian Systems written by George Zaslavsky and published by World Scientific. This book was released on 1998-07-04 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to familiarise the reader with the essential properties of the chaotic dynamics of Hamiltonian systems. It includes unique material on separatrix chaos, small nonlinearity chaos, fractional kinetics, and discussions on Maxwell's Demon and the foundation of statistical physics. Special mathematical tools not typical of physics are avoided.The book is ideally suited for all those who are actively working on the problems of dynamical chaos. It introduces the physicist to the world of Hamiltonian chaos and the mathematician to actual physical problems. The material can also be used by graduate students.
Download or read book Chaotic Diffusion in Nonlinear Hamiltonian Systems written by and published by . This book was released on 2012 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work investigates diffusion in nonlinear Hamiltonian systems. The diffusion, more precisely subdiffusion, in such systems is induced by the intrinsic chaotic behavior of trajectories and thus is called chaotic diffusion''. Its properties are studied on the example of one- or two-dimensional lattices of harmonic or nonlinear oscillators with nearest neighbor couplings. The fundamental observation is the spreading of energy for localized initial conditions. Methods of quantifying this spreading behavior are presented, including a new quantity called excitation time. This new quantity allows for a more precise analysis of the spreading than traditional methods. Furthermore, the nonlinear diffusion equation is introduced as a phenomenologic description of the spreading process and a number of predictions on the density dependence of the spreading are drawn from this equation. Two mathematical techniques for analyzing nonlinear Hamiltonian systems are introduced. The first one is based on a scaling analysis of the Hamiltonian equation...
Download or read book Chaos and Diffusion in Hamiltonian Systems written by and published by Atlantica Séguier Frontières. This book was released on 1995 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Chaotic Dynamics of Nonlinear Systems written by S. Neil Rasband and published by Courier Dover Publications. This book was released on 2015-08-19 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to the concepts, applications, theory, and technique of chaos. Suitable for advanced undergraduates and graduate students and researchers. Requires familiarity with differential equations and linear vector spaces. 1990 edition.
Download or read book Chaotic Dynamics In Hamiltonian Systems With Applications To Celestial Mechanics written by Harry Dankowicz and published by World Scientific. This book was released on 1997-12-16 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past hundred years investigators have learned the significance of complex behavior in deterministic systems. The potential applications of this discovery are as numerous as they are encouraging.This text clearly presents the mathematical foundations of chaotic dynamics, including methods and results at the forefront of current research. The book begins with a thorough introduction to dynamical systems and their applications. It goes on to develop the theory of regular and stochastic behavior in higher-degree-of-freedom Hamiltonian systems, covering topics such as homoclinic chaos, KAM theory, the Melnikov method, and Arnold diffusion. Theoretical discussions are illustrated by a study of the dynamics of small circumasteroidal grains perturbed by solar radiation pressure. With alternative derivations and proofs of established results substituted for those in the standard literature, this work serves as an important source for researchers, students and teachers.Skillfully combining in-depth mathematics and actual physical applications, this book will be of interest to the applied mathematician, the theoretical mechanical engineer and the dynamical astronomer alike.
Download or read book Hamiltonian Chaos and Fractional Dynamics written by George M. Zaslavsky and published by OUP Oxford. This book was released on 2004-12-23 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology. The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. The book does not follow the traditional scheme of most of today's literature on chaos. The intention of the author has been to put together some of the most complex and yet open problems on the general theory of chaotic systems. The importance of the discussed issues and an understanding of their origin should inspire students and researchers to touch upon some of the deepest aspects of nonlinear dynamics. The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others. It presents a new and realistic image of the origin of dynamical chaos and randomness. An understanding of the origin of randomness in dynamical systems, which cannot be of the same origin as chaos, provides new insights in the diverse fields of physics, biology, chemistry, and engineering.
Download or read book Physics Of Chaos In Hamiltonian Systems The 2nd Edition written by George Zaslavsky and published by World Scientific. This book was released on 2007-05-21 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to familiarize the reader with the essential properties of the chaotic dynamics of Hamiltonian systems by avoiding specialized mathematical tools, thus making it easily accessible to a broader audience of researchers and students. Unique material on the most intriguing and fascinating topics of unsolved and current problems in contemporary chaos theory is presented. The coverage includes: separatrix chaos; properties and a description of systems with non-ergodic dynamics; the distribution of Poincaré recurrences and their role in transport theory; dynamical models of the Maxwell's Demon, the occurrence of persistent fluctuations, and a detailed discussion of their role in the problem underlying the foundation of statistical physics; the emergence of stochastic webs in phase space and their link to space tiling with periodic (crystal type) and aperiodic (quasi-crystal type) symmetries.This second edition expands on pseudochaotic dynamics with weak mixing and the new phenomenon of fractional kinetics, which is crucial to the transport properties of chaotic motion.The book is ideally suited to all those who are actively working on the problems of dynamical chaos as well as to those looking for new inspiration in this area. It introduces the physicist to the world of Hamiltonian chaos and the mathematician to actual physical problems.The material can also be used by graduate students./a
Download or read book Dynamical Phase Transitions in Chaotic Systems written by Edson Denis Leonel and published by Springer Nature. This book was released on 2023-08-14 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses some scaling properties and characterizes two-phase transitions for chaotic dynamics in nonlinear systems described by mappings. The chaotic dynamics is determined by the unpredictability of the time evolution of two very close initial conditions in the phase space. It yields in an exponential divergence from each other as time passes. The chaotic diffusion is investigated, leading to a scaling invariance, a characteristic of a continuous phase transition. Two different types of transitions are considered in the book. One of them considers a transition from integrability to non-integrability observed in a two-dimensional, nonlinear, and area-preserving mapping, hence a conservative dynamics, in the variables action and angle. The other transition considers too the dynamics given by the use of nonlinear mappings and describes a suppression of the unlimited chaotic diffusion for a dissipative standard mapping and an equivalent transition in the suppression of Fermi acceleration in time-dependent billiards. This book allows the readers to understand some of the applicability of scaling theory to phase transitions and other critical dynamics commonly observed in nonlinear systems. That includes a transition from integrability to non-integrability and a transition from limited to unlimited diffusion, and that may also be applied to diffusion in energy, hence in Fermi acceleration. The latter is a hot topic investigated in billiard dynamics that led to many important publications in the last few years. It is a good reference book for senior- or graduate-level students or researchers in dynamical systems and control engineering, mathematics, physics, mechanical and electrical engineering.
Download or read book Complex Hamiltonian Dynamics written by Tassos Bountis and published by Springer Science & Business Media. This book was released on 2012-04-03 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores modern developments in Hamiltonian dynamical systems, focusing on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. Includes end-of-chapter exercises and challenging problems.
Download or read book Weak Chaos and Quasi Regular Patterns written by Georgin Moiseevich Zaslavskiî and published by Cambridge University Press. This book was released on 1991-04-11 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the fundamentals of chaos theory in conservative systems and provides a systematic study of the theory of transitional states of physical systems that lie between deterministic and chaotic behavior. The authors begin with the general concepts of Hamiltonian dynamics, stabililty, and chaos, and then discuss the theory of stochastic layers and webs and the numerous applications of this theory, particularly to pattern symmetry. Throughout, they are meticulous in providing a detailed presentation of the material, which enables the reader to learn the necessary computational methods and to apply them to other problems. The inclusion of computer graphics will aid understanding and the final section of the book contains a collection of patterns in art and living nature that will fascinate.
Download or read book Nonlinear Dynamics and Chaos written by J Hogan and published by CRC Press. This book was released on 2002-08-01 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear dynamics has been successful in explaining complicated phenomena in well-defined low-dimensional systems. Now it is time to focus on real-life problems that are high-dimensional or ill-defined, for example, due to delay, spatial extent, stochasticity, or the limited nature of available data. How can one understand the dynamics of such sys
Download or read book Nonlinear Dynamics and Chaotic Phenomena written by B.K Shivamoggi and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: FolJowing the formulation of the laws of mechanics by Newton, Lagrange sought to clarify and emphasize their geometrical character. Poincare and Liapunov successfuIJy developed analytical mechanics further along these lines. In this approach, one represents the evolution of all possible states (positions and momenta) by the flow in phase space, or more efficiently, by mappings on manifolds with a symplectic geometry, and tries to understand qualitative features of this problem, rather than solving it explicitly. One important outcome of this line of inquiry is the discovery that vastly different physical systems can actually be abstracted to a few universal forms, like Mandelbrot's fractal and Smale's horse-shoe map, even though the underlying processes are not completely understood. This, of course, implies that much of the observed diversity is only apparent and arises from different ways of looking at the same system. Thus, modern nonlinear dynamics 1 is very much akin to classical thermodynamics in that the ideas and results appear to be applicable to vastly different physical systems. Chaos theory, which occupies a central place in modem nonlinear dynamics, refers to a deterministic development with chaotic outcome. Computers have contributed considerably to progress in chaos theory via impressive complex graphics. However, this approach lacks organization and therefore does not afford complete insight into the underlying complex dynamical behavior. This dynamical behavior mandates concepts and methods from such areas of mathematics and physics as nonlinear differential equations, bifurcation theory, Hamiltonian dynamics, number theory, topology, fractals, and others.
Download or read book Hamiltonian Systems written by Alfredo M. Ozorio de Almeida and published by Cambridge University Press. This book was released on 1988 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hamiltonian Systems outlines the main results in the field, and considers the implications for quantum mechanics.
Download or read book Regular and Chaotic Dynamics written by A.J. Lichtenberg and published by Springer Science & Business Media. This book was released on 1992-06-24 with total page 780 pages. Available in PDF, EPUB and Kindle. Book excerpt: Text-reference for physical scientists and engineers as well as advanced graduate students treats chaotic motion in nonlinear dynamical systems. The main emphasis of the first edition of 1983 (titled Regular and stochastic motion) was on intrinsic stochasticity in Hamiltonian systems. This has been broadened to include a thorough introduction to chaotic motion in dissipative systems in the final two chapters. The treatment emphasizes physical insight rather than mathematical rigor. Annotation copyrighted by Book News, Inc., Portland, OR
Download or read book Chaos Concepts Control and Constructive Use written by Yurii Bolotin and published by Springer Science & Business Media. This book was released on 2009-08-06 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of physics has changed in character, mainly due to the passage from the analyses of linear systems to the analyses of nonlinear systems. Such a change began, it goes without saying, a long time ago but the qualitative change took place and boldly evolved after the understanding of the nature of chaos in nonlinear s- tems. The importance of these systems is due to the fact that the major part of physical reality is nonlinear. Linearity appears as a result of the simpli?cation of real systems, and often, is hardly achievable during the experimental studies. In this book, we focus our attention on some general phenomena, naturally linked with nonlinearity where chaos plays a constructive part. The ?rst chapter discusses the concept of chaos. It attempts to describe the me- ing of chaos according to the current understanding of it in physics and mat- matics. The content of this chapter is essential to understand the nature of chaos and its appearance in deterministic physical systems. Using the Turing machine, we formulate the concept of complexity according to Kolmogorov. Further, we state the algorithmic theory of Kolmogorov–Martin-Lof ̈ randomness, which gives a deep understanding of the nature of deterministic chaos. Readers will not need any advanced knowledge to understand it and all the necessary facts and de?nitions will be explained.
Download or read book The Transition to Chaos written by Linda Reichl and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: resonances. Nonlinear resonances cause divergences in conventional perturbation expansions. This occurs because nonlinear resonances cause a topological change locally in the structure of the phase space and simple perturbation theory is not adequate to deal with such topological changes. In Sect. (2.3), we introduce the concept of integrability. A sys tem is integrable if it has as many global constants of the motion as degrees of freedom. The connection between global symmetries and global constants of motion was first proven for dynamical systems by Noether [Noether 1918]. We will give a simple derivation of Noether's theorem in Sect. (2.3). As we shall see in more detail in Chapter 5, are whole classes of systems which are now known to be inte there grable due to methods developed for soliton physics. In Sect. (2.3), we illustrate these methods for the simple three-body Toda lattice. It is usually impossible to tell if a system is integrable or not just by looking at the equations of motion. The Poincare surface of section provides a very useful numerical tool for testing for integrability and will be used throughout the remainder of this book. We will illustrate the use of the Poincare surface of section for classic model of Henon and Heiles [Henon and Heiles 1964].
Download or read book From Hamiltonian Chaos to Complex Systems written by Xavier Leoncini and published by Springer Science & Business Media. This book was released on 2013-07-14 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach collects contributions on recent developments in non-linear dynamics and statistical physics with an emphasis on complex systems. This book provides a wide range of state-of-the-art research in these fields. The unifying aspect of this book is demonstration of how similar tools coming from dynamical systems, nonlinear physics, and statistical dynamics can lead to a large panorama of research in various fields of physics and beyond, most notably with the perspective of application in complex systems.
