Quasi Periodic Motions In Families Of Dynamical Systems

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Quasi-Periodic Motions in Families of Dynamical Systems

Author : Hendrik W. Broer
Publisher : Springer
ISBN 13 : 3540496130
Total Pages : 203 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Quasi-Periodic Motions in Families of Dynamical Systems by : Hendrik W. Broer

Download or read book Quasi-Periodic Motions in Families of Dynamical Systems written by Hendrik W. Broer and published by Springer. This book was released on 2009-01-25 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the phenomenon of quasi-periodic motion in dynamical systems. Such a motion in the phase space densely fills up an invariant torus. This phenomenon is most familiar from Hamiltonian dynamics. Hamiltonian systems are well known for their use in modelling the dynamics related to frictionless mechanics, including the planetary and lunar motions. In this context the general picture appears to be as follows. On the one hand, Hamiltonian systems occur that are in complete order: these are the integrable systems where all motion is confined to invariant tori. On the other hand, systems exist that are entirely chaotic on each energy level. In between we know systems that, being sufficiently small perturbations of integrable ones, exhibit coexistence of order (invariant tori carrying quasi-periodic dynamics) and chaos (the so called stochastic layers). The Kolmogorov-Arnol'd-Moser (KAM) theory on quasi-periodic motions tells us that the occurrence of such motions is open within the class of all Hamiltonian systems: in other words, it is a phenomenon persistent under small Hamiltonian perturbations. Moreover, generally, for any such system the union of quasi-periodic tori in the phase space is a nowhere dense set of positive Lebesgue measure, a so called Cantor family. This fact implies that open classes of Hamiltonian systems exist that are not ergodic. The main aim of the book is to study the changes in this picture when other classes of systems - or contexts - are considered.

Quasi-Periodic Motions in Families of Dynamical Systems

Author : Hendrik W. Broer
Publisher :
ISBN 13 : 9783662167953
Total Pages : 216 pages
Book Rating : 4.1/5 (679 download)

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Book Synopsis Quasi-Periodic Motions in Families of Dynamical Systems by : Hendrik W. Broer

Download or read book Quasi-Periodic Motions in Families of Dynamical Systems written by Hendrik W. Broer and published by . This book was released on 2014-01-15 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stable and Random Motions in Dynamical Systems

Author : Jurgen Moser
Publisher : Princeton University Press
ISBN 13 : 1400882699
Total Pages : 216 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Stable and Random Motions in Dynamical Systems by : Jurgen Moser

Download or read book Stable and Random Motions in Dynamical Systems written by Jurgen Moser and published by Princeton University Press. This book was released on 2016-03-02 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: For centuries, astronomers have been interested in the motions of the planets and in methods to calculate their orbits. Since Newton, mathematicians have been fascinated by the related N-body problem. They seek to find solutions to the equations of motion for N masspoints interacting with an inverse-square-law force and to determine whether there are quasi-periodic orbits or not. Attempts to answer such questions have led to the techniques of nonlinear dynamics and chaos theory. In this book, a classic work of modern applied mathematics, Jürgen Moser presents a succinct account of two pillars of the theory: stable and chaotic behavior. He discusses cases in which N-body motions are stable, covering topics such as Hamiltonian systems, the (Moser) twist theorem, and aspects of Kolmogorov-Arnold-Moser theory. He then explores chaotic orbits, exemplified in a restricted three-body problem, and describes the existence and importance of homoclinic points. This book is indispensable for mathematicians, physicists, and astronomers interested in the dynamics of few- and many-body systems and in fundamental ideas and methods for their analysis. After thirty years, Moser's lectures are still one of the best entrées to the fascinating worlds of order and chaos in dynamics.

Global Analysis of Dynamical Systems

Author : H.W Broer
Publisher : CRC Press
ISBN 13 : 9781420034288
Total Pages : 498 pages
Book Rating : 4.0/5 (342 download)

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Book Synopsis Global Analysis of Dynamical Systems by : H.W Broer

Download or read book Global Analysis of Dynamical Systems written by H.W Broer and published by CRC Press. This book was released on 2001-06-18 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributed by close colleagues, friends, and former students of Floris Takens, Global Analysis of Dynamical Systems is a liber amicorum dedicated to Takens for his 60th birthday. The first chapter is a reproduction of Takens's 1974 paper "Forced oscillators and bifurcations" that was previously available only as a preprint of the University of Utrecht. Among other important results, it contains the unfolding of what is now known as the Bogdanov-Takens bifurcation. The remaining chapters cover topics as diverse as bifurcation theory, Hamiltonian mechanics, homoclinic bifurcations, routes to chaos, ergodic theory, renormalization theory, and time series analysis. In its entirety, the book bears witness to the influence of Takens on the modern theory of dynamical systems and its applications. This book is a must-read for anyone interested in this active and exciting field.

Handbook of Dynamical Systems

Author : H. Broer
Publisher : Elsevier
ISBN 13 : 9780080932262
Total Pages : 560 pages
Book Rating : 4.9/5 (322 download)

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Book Synopsis Handbook of Dynamical Systems by : H. Broer

Download or read book Handbook of Dynamical Systems written by H. Broer and published by Elsevier. This book was released on 2010-11-10 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli. Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systems Highlights developments that are the foundation for future research in this field Provides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dynamical systems

Recent Trends in Dynamical Systems

Author : Andreas Johann
Publisher : Springer Science & Business Media
ISBN 13 : 3034804512
Total Pages : 616 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Recent Trends in Dynamical Systems by : Andreas Johann

Download or read book Recent Trends in Dynamical Systems written by Andreas Johann and published by Springer Science & Business Media. This book was released on 2013-09-24 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of a conference on dynamical systems held in honor of Jürgen Scheurle in January 2012. Through both original research papers and survey articles leading experts in the field offer overviews of the current state of the theory and its applications to mechanics and physics. In particular, the following aspects of the theory of dynamical systems are covered: - Stability and bifurcation - Geometric mechanics and control theory - Invariant manifolds, attractors and chaos - Fluid mechanics and elasticity - Perturbations and multiscale problems - Hamiltonian dynamics and KAM theory Researchers and graduate students in dynamical systems and related fields, including engineering, will benefit from the articles presented in this volume.

Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems

Author : Heinz Hanßmann
Publisher : Springer
ISBN 13 : 3540388966
Total Pages : 242 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems by : Heinz Hanßmann

Download or read book Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems written by Heinz Hanßmann and published by Springer. This book was released on 2006-10-18 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates that while elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Therefore, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system, absent untypical conditions or external parameters. The text moves logically from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations must be replaced by Cantor sets.

Dynamical Systems and Small Divisors

Author : Hakan Eliasson
Publisher : Springer
ISBN 13 : 3540479287
Total Pages : 207 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Dynamical Systems and Small Divisors by : Hakan Eliasson

Download or read book Dynamical Systems and Small Divisors written by Hakan Eliasson and published by Springer. This book was released on 2004-10-11 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems of stability in the theory of dynamical systems face the difficulty of small divisors. The most famous example is probably given by Kolmogorov-Arnold-Moser theory in the context of Hamiltonian systems, with many applications to physics and astronomy. Other natural small divisor problems arise considering circle diffeomorphisms or quasiperiodic Schroedinger operators. In this volume Hakan Eliasson, Sergei Kuksin and Jean-Christophe Yoccoz illustrate the most recent developments of this theory both in finite and infinite dimension. A list of open problems (including some problems contributed by John Mather and Michel Herman) has been included.

European Congress of Mathematics

Author : Carles Casacuberta
Publisher : Birkhäuser
ISBN 13 : 3034882661
Total Pages : 630 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis European Congress of Mathematics by : Carles Casacuberta

Download or read book European Congress of Mathematics written by Carles Casacuberta and published by Birkhäuser. This book was released on 2012-12-06 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician.

Dynamical Systems

Author : Yunping Jiang
Publisher : World Scientific
ISBN 13 : 9814543276
Total Pages : 372 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Dynamical Systems by : Yunping Jiang

Download or read book Dynamical Systems written by Yunping Jiang and published by World Scientific. This book was released on 1999-12-16 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the proceedings of the International Conference on Dynamical Systems in Honor of Prof. Liao Shantao (1920–97). The Third World Academy of Sciences awarded the first ever mathematics prize in 1985 to Prof. Liao in recognition of his foundational work in differentiable dynamical systems and his work in periodic transformation of spheres. The conference was held in Beijing in August 1998. There were about 90 participants, and nearly 60 talks were delivered. The topics covered include differentiable dynamics, topological dynamics, hamiltonian dynamics, complex dynamics, ergodic and stochastic dynamics, and fractals theory. Dynamical systems is a field with many difficult problems, and techniques are being developed to deal with those problems. This volume contains original studies of great mathematical depth and presents some of the fascinating numerical experiments. Contents: The Dynamics of the Henon-Like Maps (Y-L Cao)Nonchaos for Substitution Minimal Systems (Q-J Fan et al.)A Note on the Obstruction Sets of Discrete Systems (S-B Gan)Topological Pressure of Continuous Flows Without Fixed Points (L-F He et al.)Nonlinearity, Quasisymmetry, Differentiability, and Rigidity in One-Dimensional Dynamics (Y-P Jiang)The Stability of the Equilibrium of Planar Hamiltonian Systems (B Liu)Existence and Uniqueness of Analytic Solutions of Iterative Functional Equations (J-H Mai & X-H Liu)On Bimodal Collet-Eckmann Maps (L-Y Wang)An Introduction to the C1 Connecting Lemma (L Wen)Partial Entropy, Bundle-Like Entropy and Topological Entropy (F-P Zeng)and other papers Readership: Research mathematicians and graduates in analysis and differential equations. Keywords:Dynamical Systems;Periodic Transformation;Topological Dynamics;Hamiltonian Dynamics;Complex Dynamics;Ergodic;Stochastic Dynamics;Fractals Theory;Henon-Like Maps;Fixed Points;Nonlinearity;Quasisymmetry;Planar Hamiltonian Systems;Analytic Solutions;Iterative Functional Equations;Partial Entropy;Bundle-Like Entropy;Topological Entropy

Perturbation Theory

Author : Giuseppe Gaeta
Publisher : Springer Nature
ISBN 13 : 1071626213
Total Pages : 601 pages
Book Rating : 4.0/5 (716 download)

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Book Synopsis Perturbation Theory by : Giuseppe Gaeta

Download or read book Perturbation Theory written by Giuseppe Gaeta and published by Springer Nature. This book was released on 2022-12-16 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare’-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.

Measure and Capacity of Wandering Domains in Gevrey Near-Integrable Exact Symplectic Systems

Author : Laurent Lazzarini
Publisher : American Mathematical Soc.
ISBN 13 : 147043492X
Total Pages : 106 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Measure and Capacity of Wandering Domains in Gevrey Near-Integrable Exact Symplectic Systems by : Laurent Lazzarini

Download or read book Measure and Capacity of Wandering Domains in Gevrey Near-Integrable Exact Symplectic Systems written by Laurent Lazzarini and published by American Mathematical Soc.. This book was released on 2019-02-21 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: A wandering domain for a diffeomorphism of is an open connected set such that for all . The authors endow with its usual exact symplectic structure. An integrable diffeomorphism, i.e., the time-one map of a Hamiltonian which depends only on the action variables, has no nonempty wandering domains. The aim of this paper is to estimate the size (measure and Gromov capacity) of wandering domains in the case of an exact symplectic perturbation of , in the analytic or Gevrey category. Upper estimates are related to Nekhoroshev theory; lower estimates are related to examples of Arnold diffusion. This is a contribution to the “quantitative Hamiltonian perturbation theory” initiated in previous works on the optimality of long term stability estimates and diffusion times; the emphasis here is on discrete systems because this is the natural setting to study wandering domains.

Unfoldings and Bifurcations of Quasi-Periodic Tori

Author : Hendrik Wolter Broer
Publisher : American Mathematical Soc.
ISBN 13 : 082182483X
Total Pages : 175 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Unfoldings and Bifurcations of Quasi-Periodic Tori by : Hendrik Wolter Broer

Download or read book Unfoldings and Bifurcations of Quasi-Periodic Tori written by Hendrik Wolter Broer and published by American Mathematical Soc.. This book was released on 1990 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt:

EQUADIFF 2003

Author : Freddy Dumortier
Publisher : World Scientific
ISBN 13 : 9814480916
Total Pages : 1184 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis EQUADIFF 2003 by : Freddy Dumortier

Download or read book EQUADIFF 2003 written by Freddy Dumortier and published by World Scientific. This book was released on 2005-02-23 with total page 1184 pages. Available in PDF, EPUB and Kindle. Book excerpt: ' This comprehensive volume contains the state of the art on ODE's and PDE's of different nature, functional differential equations, delay equations, and others, mostly from the dynamical systems point of view. A broad range of topics are treated through contributions by leading experts of their fields, presenting the most recent developments. A large variety of techniques are being used, stressing geometric, topological, ergodic and numerical aspects. The scope of the book is wide, ranging from pure mathematics to various applied fields. Examples of the latter are provided by subjects from earth and life sciences, classical mechanics and quantum-mechanics, among others. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings) • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents: Computational Aspects of Differential Equations and ApplicationsWater WavesTopological and Variational MethodsQualitative Theory of Nonlinear Parabolic and Elliptic EquationsAround Hilbert's 16th ProblemNavier–Stokes Equations and Reaction Diffusion EquationsHyperbolic Dynamics and BeyondSymmetry and MechanicsShock Waves and Conservation LawsNonlinear Elliptic Partial Differential EquationsAlgebraic Aspects and Optimisation in Dynamical SystemsCase Studies in Theoretical Interpretation of Numerical ExperimentsInfinite-Dimensional DynamicsQuasiperiodicityDelay EquationsWave Stability and Pattern FormationNonautonomous DynamicsNormal Forms and Invariant ManifoldsSingular PerturbationsDifferential Geometric Foliations and FlowsHomoclinic and Heteroclinic DynamicsMathematical Aspects of Celestical Mechanics Readership: Graduate students and researchers in mathematics, especially in ODE and PDE areas. Keywords:Differential Equations;Dynamical Systems;ODE;PDE;Delay Equations;Water Waves;Hilbert''s 16th Problem'

Multiple-Time-Scale Dynamical Systems

Author : Christopher K.R.T. Jones
Publisher : Springer Science & Business Media
ISBN 13 : 1461301173
Total Pages : 278 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Multiple-Time-Scale Dynamical Systems by : Christopher K.R.T. Jones

Download or read book Multiple-Time-Scale Dynamical Systems written by Christopher K.R.T. Jones and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systems with sub-processes evolving on many different time scales are ubiquitous in applications: chemical reactions, electro-optical and neuro-biological systems, to name just a few. This volume contains papers that expose the state of the art in mathematical techniques for analyzing such systems. Recently developed geometric ideas are highlighted in this work that includes a theory of relaxation-oscillation phenomena in higher dimensional phase spaces. Subtle exponentially small effects result from singular perturbations implicit in certain multiple time scale systems. Their role in the slow motion of fronts, bifurcations, and jumping between invariant tori are all explored here. Neurobiology has played a particularly stimulating role in the development of these techniques and one paper is directed specifically at applying geometric singular perturbation theory to reveal the synchrony in networks of neural oscillators.

Regular and Chaotic Motions in Dynamic Systems

Author : A. S. Wightman
Publisher : Springer Science & Business Media
ISBN 13 : 1468412213
Total Pages : 312 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Regular and Chaotic Motions in Dynamic Systems by : A. S. Wightman

Download or read book Regular and Chaotic Motions in Dynamic Systems written by A. S. Wightman and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fifth International School ~ Mathematical Physics was held at the Ettore Majorana Centro della Culture Scientifica, Erice, Sicily, 2 to 14 July 1983. The present volume collects lecture notes on the session which was devoted to'Regular and Chaotic Motions in Dynamlcal Systems. The School was a NATO Advanced Study Institute sponsored by the Italian Ministry of Public Education, the Italian Ministry of Scientific and Technological Research and the Regional Sicilian Government. Many of the fundamental problems of this subject go back to Poincare and have been recognized in recent years as being of basic importance in a variety of physical contexts: stability of orbits in accelerators, and in plasma and galactic dynamics, occurrence of chaotic motions in the excitations of solids, etc. This period of intense interest on the part of physicists followed nearly a half a century of neglect in which research in the subject was almost entirely carried out by mathematicians. It is an in dication of the difficulty of some of the problems involved that even after a century we do not have anything like a satisfactory solution.

Averaging Methods in Nonlinear Dynamical Systems

Author : Jan A. Sanders
Publisher : Springer Science & Business Media
ISBN 13 : 0387489185
Total Pages : 447 pages
Book Rating : 4.3/5 (874 download)

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Book Synopsis Averaging Methods in Nonlinear Dynamical Systems by : Jan A. Sanders

Download or read book Averaging Methods in Nonlinear Dynamical Systems written by Jan A. Sanders and published by Springer Science & Business Media. This book was released on 2007-08-18 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Perturbation theory and in particular normal form theory has shown strong growth in recent decades. This book is a drastic revision of the first edition of the averaging book. The updated chapters represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are survey appendices on invariant manifolds. One of the most striking features of the book is the collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with illuminating diagrams.