Regular And Chaotic Dynamics
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Regular And Chaotic Dynamics
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Author : A.J. Lichtenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Regular And Chaotic Dynamics written by A.J. Lichtenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
What's in a name? The original title of our book, Regular and Stochastic Motion, was chosen to emphasize Hamiltonian dynamics and the physical motion of bodies. The new edition is more evenhanded, with considerably more discussion of dissipative systems and dynamics not involving physical motion. To reflect this partial change of emphasis, we have substituted the more general terms in our title. The common usage of the new terms clarifies the emphasis of the book. The main change in the book has been to expand the sections on dissipative dynamics, including discussion of renormalization, circle maps, intermittancy, crises, transient chaos, multifractals, reconstruction, and coupled mapping systems. These topics were either mainly in the mathemati cal literature or essentially unstudied when our first edition was written. The volume of work in these areas has surpassed that in Hamiltonian dynamics within the past few years. We have also made changes in the Hamiltonian sections, adding many new topics such as more general transformation and stability theory, connected stochasticity in two-dimensional maps, converse KAM theory, new topics in diffusion theory, and an approach to equilibrium in many dimensions. Other sections such as mapping models have been revised to take into account new perspectives. We have also corrected a number of misprints and clarified various arguments with the help of colleagues and students, some of whom we acknowledge below. We have again chosen not to treat quantum chaos, partly due to our own lack ofacquaintance with the subject.
Regular And Chaotic Dynamics
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Author : Allan J. Lichtenberg
language : en
Publisher:
Release Date : 1992-01-01
Regular And Chaotic Dynamics written by Allan J. Lichtenberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Hamiltonian systems categories.
Regular And Chaotic Dynamics
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Author : Allan Lichtenberg
language : en
Publisher:
Release Date : 2014-01-15
Regular And Chaotic Dynamics written by Allan Lichtenberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Chaotic Dynamics
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Author : Tamás Tél
language : en
Publisher: Cambridge University Press
Release Date : 2006-08-24
Chaotic Dynamics written by Tamás Tél and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-24 with Mathematics categories.
A clear introduction to chaotic phenomena for undergraduate students in science, engineering, and mathematics.
New Methods For Chaotic Dynamics
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Author : Nikolai Aleksandrovich Magnitskii
language : en
Publisher: World Scientific
Release Date : 2006
New Methods For Chaotic Dynamics written by Nikolai Aleksandrovich Magnitskii and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This book presents a new theory on the transition to dynamical chaos for two-dimensional nonautonomous, and three-dimensional, many-dimensional and infinitely-dimensional autonomous nonlinear dissipative systems of differential equations including nonlinear partial differential equations and differential equations with delay arguments. The transition is described from the Feigenbaum cascade of period doubling bifurcations of the original singular cycle to the complete or incomplete Sharkovskii subharmonic cascade of bifurcations of stable limit cycles with arbitrary period and finally to the complete or incomplete homoclinic cascade of bifurcations. The book presents a distinct view point on the principles of formation, scenarios of occurrence and ways of control of chaotic motion in nonlinear dissipative dynamical systems. All theoretical results and conclusions of the theory are strictly proved and confirmed by numerous examples, illustrations and numerical calculations. Sample Chapter(s). Chapter 1: Systems of Ordinary Differential Equations (1,736 KB). Contents: Systems of Ordinary Differential Equations; Bifurcations in Nonlinear Systems of Ordinary Differential Equations; Chaotic Systems of Ordinary Differential Equations; Principles of the Theory of Dynamical Chaos in Dissipative Systems of Ordinary Differential Equations; Dynamical Chaos in Infinitely-Dimensional Systems of Differential Equations; Chaos Control in Systems of Differential Equations. Readership: Graduate students and researchers in complex and chaotic dynamical systems.
Regular And Chaotic Dynamics
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Author :
language : en
Publisher:
Release Date :
Regular And Chaotic Dynamics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Nonlinear Dynamics
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Author : Muthusamy Lakshmanan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Dynamics written by Muthusamy Lakshmanan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Integrability, chaos and patterns are three of the most important concepts in nonlinear dynamics. These are covered in this book from fundamentals to recent developments. The book presents a self-contained treatment of the subject to suit the needs of students, teachers and researchers in physics, mathematics, engineering and applied sciences who wish to gain a broad knowledge of nonlinear dynamics. It describes fundamental concepts, theoretical procedures, experimental and numerical techniques and technological applications of nonlinear dynamics. Numerous examples and problems are included to facilitate the understanding of the concepts and procedures described. In addition to 16 chapters of main material, the book contains 10 appendices which present in-depth mathematical formulations involved in the analysis of various nonlinear systems.
Rigid Body Dynamics
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Author : Alexey Borisov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-12-03
Rigid Body Dynamics written by Alexey Borisov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-03 with Science categories.
This book provides an up-to-date overview of results in rigid body dynamics, including material concerned with the analysis of nonintegrability and chaotic behavior in various related problems. The wealth of topics covered makes it a practical reference for researchers and graduate students in mathematics, physics and mechanics. Contents Rigid Body Equations of Motion and Their Integration The Euler – Poisson Equations and Their Generalizations The Kirchhoff Equations and Related Problems of Rigid Body Dynamics Linear Integrals and Reduction Generalizations of Integrability Cases. Explicit Integration Periodic Solutions, Nonintegrability, and Transition to Chaos Appendix A : Derivation of the Kirchhoff, Poincaré – Zhukovskii, and Four-Dimensional Top Equations Appendix B: The Lie Algebra e(4) and Its Orbits Appendix C: Quaternion Equations and L-A Pair for the Generalized Goryachev – Chaplygin Top Appendix D: The Hess Case and Quantization of the Rotation Number Appendix E: Ferromagnetic Dynamics in a Magnetic Field Appendix F: The Landau – Lifshitz Equation, Discrete Systems, and the Neumann Problem Appendix G: Dynamics of Tops and Material Points on Spheres and Ellipsoids Appendix H: On the Motion of a Heavy Rigid Body in an Ideal Fluid with Circulation Appendix I: The Hamiltonian Dynamics of Self-gravitating Fluid and Gas Ellipsoids
Nonlinear Dynamics And Chaos
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Author : Steven H. Strogatz
language : en
Publisher: CRC Press
Release Date : 2018-05-04
Nonlinear Dynamics And Chaos written by Steven H. Strogatz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Mathematics categories.
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Recent Trends In Chaotic Nonlinear And Complex Dynamics
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Author : Jan Awrejcewicz
language : en
Publisher: World Scientific
Release Date : 2021-07-26
Recent Trends In Chaotic Nonlinear And Complex Dynamics written by Jan Awrejcewicz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-26 with Science categories.
In recent years, enormous progress has been made on nonlinear dynamics particularly on chaos and complex phenomena. This unique volume presents the advances made in theory, analysis, numerical simulation and experimental realization, promising novel practical applications on various topics of current interest on chaos and related fields of nonlinear dynamics.Particularly, the focus is on the following topics: synchronization vs. chaotic phenomena, chaos and its control in engineering dynamical systems, fractal-based dynamics, uncertainty and unpredictability measures vs. chaos, Hamiltonian systems and systems with time delay, local/global stability, bifurcations and their control, applications of machine learning to chaos, nonlinear vibrations of lumped mass mechanical/mechatronic systems (rigid body and coupled oscillator dynamics) governed by ODEs and continuous structural members (beams, plates, shells) vibrations governed by PDEs, patterns formation, chaos in micro- and nano-mechanical systems, chaotic reduced-order models, energy absorption/harvesting from chaotic, chaos vs. resonance phenomena, chaos exhibited by discontinuous systems, chaos in lab experiments.The present volume forms an invaluable source on recent trends in chaotic and complex dynamics for any researcher and newcomers to the field of nonlinear dynamics.