Hamiltonian Chaos Beyond The Kam Theory

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Hamiltonian Chaos Beyond the KAM Theory

Author : Albert C. J. Luo,Valentin Afraimovich
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 55,8 Mb
Release : 2011-01-04
Category : Science
ISBN : 9783642127182

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Hamiltonian Chaos Beyond the KAM Theory by Albert C. J. Luo,Valentin Afraimovich Pdf

“Hamiltonian Chaos Beyond the KAM Theory: Dedicated to George M. Zaslavsky (1935—2008)” covers the recent developments and advances in the theory and application of Hamiltonian chaos in nonlinear Hamiltonian systems. The book is dedicated to Dr. George Zaslavsky, who was one of three founders of the theory of Hamiltonian chaos. Each chapter in this book was written by well-established scientists in the field of nonlinear Hamiltonian systems. The development presented in this book goes beyond the KAM theory, and the onset and disappearance of chaos in the stochastic and resonant layers of nonlinear Hamiltonian systems are predicted analytically, instead of qualitatively. The book is intended for researchers in the field of nonlinear dynamics in mathematics, physics and engineering. Dr. Albert C.J. Luo is a Professor at Southern Illinois University Edwardsville, USA. Dr. Valentin Afraimovich is a Professor at San Luis Potosi University, Mexico.

Hamiltonian Chaos Beyond the KAM Theory

Author : Albert C. J. Luo
Publisher : Unknown
Page : 292 pages
File Size : 52,6 Mb
Release : 2010
Category : Chaotic behavior in systems
ISBN : 7040291878

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Hamiltonian Chaos Beyond the KAM Theory by Albert C. J. Luo Pdf

Chaotic Dynamics in Hamiltonian Systems

Author : Harry Dankowicz
Publisher : World Scientific
Page : 224 pages
File Size : 47,8 Mb
Release : 1997-12-16
Category : Science
ISBN : 9789814497107

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Chaotic Dynamics in Hamiltonian Systems by Harry Dankowicz Pdf

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. Contents:IntroductionHamiltonian SystemsHomoclinic OrbitsThe Perturbation ApproachApplication — Radiation Pressure IGeometry and Dynamics in Many Degrees-of-FreedomApplication — Radiation Pressure IIOutlookIndex Readership: Students and researchers in dynamical systems, classical mechanics and dynamical astronomy. keywords:Chaos;Dynamical Systems;Hamiltonian Systems;Hamiltonian Mechanics;Celestial Mechanics;Radiation Pressure;Arnold Diffusion;Melnikov's Method

The Physics of Chaos in Hamiltonian Systems

Author : George M. Zaslavsky
Publisher : World Scientific
Page : 337 pages
File Size : 55,6 Mb
Release : 2007
Category : Science
ISBN : 9781860947957

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The Physics of Chaos in Hamiltonian Systems by George M. Zaslavsky Pdf

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 Poincar‚ 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.

Hamiltonian Chaos and Fractional Dynamics

Author : George M. Zaslavsky,Georgij Moiseevič Zaslavskij
Publisher : Oxford University Press on Demand
Page : 436 pages
File Size : 53,5 Mb
Release : 2005
Category : Mathematics
ISBN : 9780198526049

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Hamiltonian Chaos and Fractional Dynamics by George M. Zaslavsky,Georgij Moiseevič Zaslavskij Pdf

This books gives a realistic contemporary image of Hamiltonian dynamics, dealing with the basic principles of the Hamiltonian theory of chaos in addition to very recent and unusual applications of nonlinear dynamics and the fractality of dynamics.

The Many Facets of Complexity Science

Author : Dimitri Volchenkov
Publisher : Springer Nature
Page : 210 pages
File Size : 41,5 Mb
Release : 2021-08-30
Category : Science
ISBN : 9789811628535

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The Many Facets of Complexity Science by Dimitri Volchenkov Pdf

This book explores recent developments in theoretical research and data analysis of real-world complex systems, organized in three parts, namely Entropy, information, and complexity functions Multistability, oscillations, and rhythmic synchronization Diffusions, rotation, and convection in fluids The collection of works devoted to the memory of Professor Valentin Afraimovich provides a deep insight into the recent developments in complexity science by introducing new concepts, methods, and applications in nonlinear dynamical systems covering physical problems and mathematical modelling relevant to economics, genetics, engineering vibrations, as well as classic problems in physics, fluid and climate dynamics, and urban dynamics. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering. It can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists, and urban planners.

The Physics of Chaos in Hamiltonian Systems

Author : George M Zaslavsky
Publisher : World Scientific
Page : 328 pages
File Size : 50,5 Mb
Release : 2007-05-21
Category : Science
ISBN : 9781908979230

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The Physics of Chaos in Hamiltonian Systems by George M Zaslavsky Pdf

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. Contents:Discrete and Continuous ModelsSeparatrix ChaosThe Phase Space of ChaosNonlinearity Versus PerturbationFractals and ChaosPoincaré Recurrences and Fractal TimeChaos and Foundation of Statistical PhysicsChaos and SymmetryMore Degrees of FreedomNormal and Anomalous KineticsFractional KineticsWeak Chaos and Pseudochaos Readership: Graduate students and researchers in physics, mathematics, engineering, chemistry and biophysics. Keywords:Billiards;Separatrix Chaos;Fractal Properties;Stochastic Webs;Kinetics;Chaotic DynamicsKey Features:New sections on the islands in stochastic sea, billiards, persistent fluctuations, and log-periodicityIncludes a new chapter on weak chaos and pseudochaosUseful for graduate and undergraduate courses on the theory of chaosReviews:Reviews of the First Edition:“George Zaslavsky develops ‘fractional kinetics’ in an attempt to give a smoothed, but nondiffusive, description. This phenomenological description captures some aspects of the stickiness of islands, but I believe its mathematical justification remains elusive. Perhaps that is an excellent reason to read this book.”Nature “The book is useful for scientists who are actively working on the problems of dynamical chaos … The material can also be used as a textbook for a graduate course on new and emerging directions in Hamiltonian chaos theory.”Zentralblatt MATH

Complex Systems

Author : Albert C. J. Luo,Jian-Qiao Sun
Publisher : Springer Science & Business Media
Page : 381 pages
File Size : 48,5 Mb
Release : 2011-12-01
Category : Science
ISBN : 9783642175930

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Complex Systems by Albert C. J. Luo,Jian-Qiao Sun Pdf

"Complex Systems: Fractionality, Time-delay and Synchronization" covers the most recent developments and advances in the theory and application of complex systems in these areas. Each chapter was written by scientists highly active in the field of complex systems. The book discusses a new treatise on fractional dynamics and control, as well as the new methods for differential delay systems and control. Lastly, a theoretical framework for the complexity and synchronization of complex system is presented. The book is intended for researchers in the field of nonlinear dynamics in mathematics, physics and engineering. It can also serve as a reference book for graduate students in physics, applied mathematics and engineering. Dr. Albert C.J. Luo is a Professor at Southern Illinois University Edwardsville, USA. Dr. Jian-Qiao Sun is a Professor at the University of California, Merced, USA.

Fractional Dynamics

Author : Vasily E. Tarasov
Publisher : Springer Science & Business Media
Page : 504 pages
File Size : 52,8 Mb
Release : 2011-01-04
Category : Science
ISBN : 9783642140037

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Fractional Dynamics by Vasily E. Tarasov Pdf

"Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and an Associate Professor at Applied Mathematics and Physics Department of Moscow Aviation Institute.

Long-range Interactions, Stochasticity and Fractional Dynamics

Author : Albert C. J. Luo,Valentin Afraimovich
Publisher : Springer Science & Business Media
Page : 327 pages
File Size : 48,5 Mb
Release : 2011-01-04
Category : Science
ISBN : 9783642123436

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Long-range Interactions, Stochasticity and Fractional Dynamics by Albert C. J. Luo,Valentin Afraimovich Pdf

In memory of Dr. George Zaslavsky, "Long-range Interactions, Stochasticity and Fractional Dynamics" covers the recent developments of long-range interaction, fractional dynamics, brain dynamics and stochastic theory of turbulence, each chapter was written by established scientists in the field. The book is dedicated to Dr. George Zaslavsky, who was one of three founders of the theory of Hamiltonian chaos. The book discusses self-similarity and stochasticity and fractionality for discrete and continuous dynamical systems, as well as long-range interactions and diluted networks. A comprehensive theory for brain dynamics is also presented. In addition, the complexity and stochasticity for soliton chains and turbulence are addressed. The book is intended for researchers in the field of nonlinear dynamics in mathematics, physics and engineering. Dr. Albert C.J. Luo is a Professor at Southern Illinois University Edwardsville, USA. Dr. Valentin Afraimovich is a Professor at San Luis Potosi University, Mexico.

Instabilities and Nonequilibrium Structures III

Author : E. Tirapegui,W. Zeller
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401134422

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Instabilities and Nonequilibrium Structures III by E. Tirapegui,W. Zeller Pdf

Proceedings of the 3rd Workshop on Instabilities and Nonequilibrium Structures

Nonlinear Deformable-body Dynamics

Author : Albert C. J. Luo
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 44,9 Mb
Release : 2011-06-08
Category : Science
ISBN : 9783642121364

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Nonlinear Deformable-body Dynamics by Albert C. J. Luo Pdf

"Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics. Dr. Albert C.J. Luo is a Professor of Mechanical Engineering at Southern Illinois University, Edwardsville, IL, USA. Professor Luo is an internationally recognized scientist in the field of nonlinear dynamics in dynamical systems and deformable solids.

Galileo Unbound

Author : David D. Nolte
Publisher : Oxford University Press
Page : 384 pages
File Size : 45,6 Mb
Release : 2018-07-12
Category : Science
ISBN : 9780192528506

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Galileo Unbound by David D. Nolte Pdf

Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

Chaos and Diffusion in Hamiltonian Systems

Author : Anonim
Publisher : Atlantica Séguier Frontières
Page : 306 pages
File Size : 42,8 Mb
Release : 1995
Category : Chaotic behavior in systems
ISBN : 2863321900

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Chaos and Diffusion in Hamiltonian Systems by Anonim Pdf

Advances in Dynamics, Patterns, Cognition

Author : Igor S. Aranson,Arkady Pikovsky,Nikolai F. Rulkov,Lev S. Tsimring
Publisher : Springer
Page : 336 pages
File Size : 46,7 Mb
Release : 2017-05-02
Category : Technology & Engineering
ISBN : 9783319536736

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Advances in Dynamics, Patterns, Cognition by Igor S. Aranson,Arkady Pikovsky,Nikolai F. Rulkov,Lev S. Tsimring Pdf

This book focuses on recent progress in complexity research based on the fundamental nonlinear dynamical and statistical theory of oscillations, waves, chaos, and structures far from equilibrium. Celebrating seminal contributions to the field by Prof. M. I. Rabinovich of the University of California at San Diego, this volume brings together perspectives on both the fundamental aspects of complexity studies, as well as in applications in different fields ranging from granular patterns to understanding of the cognitive brain and mind dynamics. The slate of world-class authors review recent achievements that together present a broad and coherent coverage of modern research in complexity greater than the sum of its parts.