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Lectures On Lyapunov Exponents
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Book Synopsis Lectures on Lyapunov Exponents by : Marcelo Viana
Download or read book Lectures on Lyapunov Exponents written by Marcelo Viana and published by Cambridge University Press. This book was released on 2014-07-24 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the fundamental aspects of the classical theory and introduces significant recent developments. Based on the author's graduate course.
Book Synopsis Lyapunov Exponents by : Ludwig Arnold
Download or read book Lyapunov Exponents written by Ludwig Arnold and published by Springer. This book was released on 2006-11-14 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the predecessor to this volume (LNM 1186, Eds. L. Arnold, V. Wihstutz)appeared in 1986, significant progress has been made in the theory and applications of Lyapunov exponents - one of the key concepts of dynamical systems - and in particular, pronounced shifts towards nonlinear and infinite-dimensional systems and engineering applications are observable. This volume opens with an introductory survey article (Arnold/Crauel) followed by 26 original (fully refereed) research papers, some of which have in part survey character. From the Contents: L. Arnold, H. Crauel: Random Dynamical Systems.- I.Ya. Goldscheid: Lyapunov exponents and asymptotic behaviour of the product of random matrices.- Y. Peres: Analytic dependence of Lyapunov exponents on transition probabilities.- O. Knill: The upper Lyapunov exponent of Sl (2, R) cocycles:Discontinuity and the problem of positivity.- Yu.D. Latushkin, A.M. Stepin: Linear skew-product flows and semigroups of weighted composition operators.- P. Baxendale: Invariant measures for nonlinear stochastic differential equations.- Y. Kifer: Large deviationsfor random expanding maps.- P. Thieullen: Generalisation du theoreme de Pesin pour l' -entropie.- S.T. Ariaratnam, W.-C. Xie: Lyapunov exponents in stochastic structural mechanics.- F. Colonius, W. Kliemann: Lyapunov exponents of control flows.
Book Synopsis Six Lectures on Dynamical Systems by : B Aulbach
Download or read book Six Lectures on Dynamical Systems written by B Aulbach and published by World Scientific. This book was released on 1996-05-15 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of six articles covering different facets of the mathematical theory of dynamical systems. The topics range from topological foundations through invariant manifolds, decoupling, perturbations and computations to control theory. All contributions are based on a sound mathematical analysis. Some of them provide detailed proofs while others are of a survey character. In any case, emphasis is put on motivation and guiding ideas. Many examples are included. The papers of this volume grew out of a tutorial workshop for graduate students in mathematics held at the University of Augsburg. Each of the contributions is self-contained and provides an in-depth insight into some topic of current interest in the mathematical theory of dynamical systems. The text is suitable for courses and seminars on a graduate student level. Contents:Dynamical Systems: The Topological Foundations (E Akin)Integral Manifolds for Carathéodory Type Differential Equations in Banach Spaces (B Aulbach & T Wanner)Control Theory and Dynamical Systems (F Colonius & W Kliemann)Shadowing in Discrete Dynamical Systems (B A Coomes, H Koçak & K J Palmer)Perturbation of Invariant Manifolds of Ordinary Differential Equations (G Osipenko & E Ershov)The Reduction of Discrete Dynamical and Semidynamical Systems in Metric Spaces (A Reinfelds) Readership: Research mathematicians, graduate students in pure and applied mathematics and readers from applied sciences and engineering. keywords:Workshop;Dynamical Systems;Augsburg (Germany);Lectures
Book Synopsis Local Lyapunov Exponents by : Wolfgang Siegert
Download or read book Local Lyapunov Exponents written by Wolfgang Siegert and published by Springer Science & Business Media. This book was released on 2009 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Establishing a new concept of local Lyapunov exponents the author brings together two separate theories, namely Lyapunov exponents and the theory of large deviations. Specifically, a linear differential system is considered which is controlled by a stochastic process that during a suitable noise-intensity-dependent time is trapped near one of its so-called metastable states. The local Lyapunov exponent is then introduced as the exponential growth rate of the linear system on this time scale. Unlike classical Lyapunov exponents, which involve a limit as time increases to infinity in a fixed system, here the system itself changes as the noise intensity converges, too.
Book Synopsis Lectures on Chaotic Dynamical Systems by : Valentin Senderovich Afraĭmovich
Download or read book Lectures on Chaotic Dynamical Systems written by Valentin Senderovich Afraĭmovich and published by American Mathematical Soc.. This book was released on 2003 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic concepts Zero-dimensional dynamics One-dimensional dynamics Two-dimensional dynamics Systems with 1.5 degrees of freedom Systems generated by three-dimensional vector fields Lyapunov exponents Appendix Bibliography Index.
Book Synopsis Lyapunov Exponents and Smooth Ergodic Theory by : Luis Barreira
Download or read book Lyapunov Exponents and Smooth Ergodic Theory written by Luis Barreira and published by American Mathematical Soc.. This book was released on 2002 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The authors consider several nontrivial examples of dynamical systems with nonzero Lyapunov exponents to illustrate some basic methods and ideas of the theory.".
Book Synopsis Lyapunov Exponents of Linear Cocycles by : Pedro Duarte
Download or read book Lyapunov Exponents of Linear Cocycles written by Pedro Duarte and published by Springer. This book was released on 2016-03-21 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this monograph is to present a general method of proving continuity of Lyapunov exponents of linear cocycles. The method uses an inductive procedure based on a general, geometric version of the Avalanche Principle. The main assumption required by this method is the availability of appropriate large deviation type estimates for quantities related to the iterates of the base and fiber dynamics associated with the linear cocycle. We establish such estimates for various models of random and quasi-periodic cocycles. Our method has its origins in a paper of M. Goldstein and W. Schlag. Our present work expands upon their approach in both depth and breadth. We conclude this monograph with a list of related open problems, some of which may be treated using a similar approach.
Book Synopsis Lyapunov Exponents by : Luís Barreira
Download or read book Lyapunov Exponents written by Luís Barreira and published by Birkhäuser. This book was released on 2017-12-30 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a self-contained introduction to the theory of Lyapunov exponents and its applications, mainly in connection with hyperbolicity, ergodic theory and multifractal analysis. It discusses the foundations and some of the main results and main techniques in the area, while also highlighting selected topics of current research interest. With the exception of a few basic results from ergodic theory and the thermodynamic formalism, all the results presented include detailed proofs. The book is intended for all researchers and graduate students specializing in dynamical systems who are looking for a comprehensive overview of the foundations of the theory and a sample of its applications.
Book Synopsis New Trends in Lyapunov Exponents by : João Lopes Dias
Download or read book New Trends in Lyapunov Exponents written by João Lopes Dias and published by Springer Nature. This book was released on 2023-11-29 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents peer-reviewed surveys on new developments in the study of Lyapunov exponents in dynamical systems and its applications to other areas, such as mathematical physics. Written by leading experts in their fields, the contributions are based upon the presentations given by invited speakers at the “New Trends in Lyapunov Exponents” workshop held in Lisbon, Portugal, February 7–11, 2022. The works focus on the concept of Lyapunov exponents in their various manifestations in dynamical systems along with their applications to mathematical physics and other areas of mathematics. The papers reflect the spirit of the conference of promoting new connections among different subjects in dynamical systems. This volume aims primarily at researchers and graduate students working in dynamical systems and related fields, serving as an introduction to active fields of research and as a review of recent results as well.
Book Synopsis Lyapunov Exponents by : Luís Barreira
Download or read book Lyapunov Exponents written by Luís Barreira and published by . This book was released on 2017 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a self-contained introduction to the theory of Lyapunov exponents and its applications, mainly in connection with hyperbolicity, ergodic theory and multifractal analysis. It discusses the foundations and some of the main results and main techniques in the area, while also highlighting selected topics of current research interest. With the exception of a few basic results from ergodic theory and the thermodynamic formalism, all the results presented include detailed proofs. The book is intended for all researchers and graduate students specializing in dynamical systems who are looking for a comprehensive overview of the foundations of the theory and a sample of its applications.
Book Synopsis Chaos Detection and Predictability by : Charalampos (Haris) Skokos
Download or read book Chaos Detection and Predictability written by Charalampos (Haris) Skokos and published by Springer. This book was released on 2016-03-04 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distinguishing chaoticity from regularity in deterministic dynamical systems and specifying the subspace of the phase space in which instabilities are expected to occur is of utmost importance in as disparate areas as astronomy, particle physics and climate dynamics. To address these issues there exists a plethora of methods for chaos detection and predictability. The most commonly employed technique for investigating chaotic dynamics, i.e. the computation of Lyapunov exponents, however, may suffer a number of problems and drawbacks, for example when applied to noisy experimental data. In the last two decades, several novel methods have been developed for the fast and reliable determination of the regular or chaotic nature of orbits, aimed at overcoming the shortcomings of more traditional techniques. This set of lecture notes and tutorial reviews serves as an introduction to and overview of modern chaos detection and predictability techniques for graduate students and non-specialists. The book covers theoretical and computational aspects of traditional methods to calculate Lyapunov exponents, as well as of modern techniques like the Fast (FLI), the Orthogonal (OFLI) and the Relative (RLI) Lyapunov Indicators, the Mean Exponential Growth factor of Nearby Orbits (MEGNO), the Smaller (SALI) and the Generalized (GALI) Alignment Index and the ‘0-1’ test for chaos.
Book Synopsis Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds by : Mark Pollicott
Download or read book Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds written by Mark Pollicott and published by Cambridge University Press. This book was released on 1993-02-04 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes provide a unique introduction to Pesin theory and its applications.
Book Synopsis Microscopic And Macroscopic Simulation Techniques: Kharagpur Lectures by : Hoover William Graham
Download or read book Microscopic And Macroscopic Simulation Techniques: Kharagpur Lectures written by Hoover William Graham and published by World Scientific. This book was released on 2018-03-13 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to provide an example-based education in numerical methods for atomistic and continuum simulations of systems at and away from equilibrium. The focus is on nonequilibrium systems, stressing the use of tools from dynamical systems theory for their analysis. Lyapunov instability and fractal dimensionality are introduced and algorithms for their analysis are detailed. The book is intended to be self-contained and accessible to students who are comfortable with calculus and differential equations. The wide range of topics covered will provide students, researchers and academics with effective tools for formulating and solving interesting problems, both atomistic and continuum. The detailed description of the use of thermostats to control nonequilibrium systems will help readers in writing their own programs rather than being saddled with packaged software. Contents: Mechanics, Molecular Dynamics, and Gibbs' Statistical Mechanics Numerical Integration and Error Analysis Molecular Dynamics with Thermostats Simple Systems with Thermal Constraints Ergodicity and Its Importance in Small Systems Equilibrium Thermodynamics + Nonequilibrium Hydrodynamics Statistical Mechanics of Small Systems Microscopic Reversibility, Macroscopic Irreversibility Lyapunov Instability, Fractals, and Chaos I Lyapunov Instability, Fractals, and Chaos II Smooth-Particle Continuum Mechanics Epilogue Readership: Undergraduate, graduate students, researchers focusing on statistical mechanics and numerical simulation. Keywords: Numerical Methods;Simulation;Nonequilibrium;Molecular Dynamics;Continuum Mechanics;Statistical Mechanics;Chaos;Lyapunov Instability;Hydrodynamics;ThermodynamicsReview: Key Features: Three useful areas covered — treatment of control variables such as thermostats and ergostats, dynamical system analysis and the use of smooth particle techniques for analyzing molecular dynamics, and the solution of continuum problems
Book Synopsis Collected Lectures on the Preservation of Stability Under Discretization by : Donald J. Estep
Download or read book Collected Lectures on the Preservation of Stability Under Discretization written by Donald J. Estep and published by SIAM. This book was released on 2002-01-01 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 13 lectures are intended to be accessible to new graduate students of mathematics, sacrificing some detail in order to offer an accessible introduction to the fundamentals of stability that can provide a foundation for further study. Presenters from the US and Britain cover preserving qualitative stability features and structural stability, and investigating physical stability and model stability. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Introduction to Smooth Ergodic Theory by : Luís Barreira
Download or read book Introduction to Smooth Ergodic Theory written by Luís Barreira and published by American Mathematical Society. This book was released on 2023-04-28 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and the second discusses more advanced topics. In particular, the book describes the general theory of Lyapunov exponents and its applications to the stability theory of differential equations, the concept of nonuniform hyperbolicity, stable manifold theory (with emphasis on absolute continuity of invariant foliations), and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. A detailed description of all the basic examples of conservative systems with nonzero Lyapunov exponents, including the geodesic flows on compact surfaces of nonpositive curvature, is also presented. There are more than 80 exercises. The book is aimed at graduate students specializing in dynamical systems and ergodic theory as well as anyone who wishes to get a working knowledge of smooth ergodic theory and to learn how to use its tools. It can also be used as a source for special topics courses on nonuniform hyperbolicity. The only prerequisite for using this book is a basic knowledge of real analysis, measure theory, differential equations, and topology, although the necessary background definitions and results are provided. In this second edition, the authors improved the exposition and added more exercises to make the book even more student-oriented. They also added new material to bring the book more in line with the current research in dynamical systems.
Book Synopsis Smooth Ergodic Theory and Its Applications by : A. B. Katok
Download or read book Smooth Ergodic Theory and Its Applications written by A. B. Katok and published by American Mathematical Soc.. This book was released on 2001 with total page 895 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past decade, there have been several major new developments in smooth ergodic theory, which have attracted substantial interest to the field from mathematicians as well as scientists using dynamics in their work. In spite of the impressive literature, it has been extremely difficult for a student-or even an established mathematician who is not an expert in the area-to acquire a working knowledge of smooth ergodic theory and to learn how to use its tools. Accordingly, the AMS Summer Research Institute on Smooth Ergodic Theory and Its Applications (Seattle, WA) had a strong educational component, including ten mini-courses on various aspects of the topic that were presented by leading experts in the field. This volume presents the proceedings of that conference. Smooth ergodic theory studies the statistical properties of differentiable dynamical systems, whose origin traces back to the seminal works of Poincare and later, many great mathematicians who made contributions to the development of the theory. The main topic of this volume, smooth ergodic theory, especially the theory of nonuniformly hyperbolic systems, provides the principle paradigm for the rigorous study of complicated or chaotic behavior in deterministic systems. This paradigm asserts that if a non-linear dynamical system exhibits sufficiently pronounced exponential behavior, then global properties of the system can be deduced from studying the linearized system. One can then obtain detailed information on topological properties (such as the growth of periodic orbits, topological entropy, and dimension of invariant sets including attractors), as well as statistical properties (such as the existence of invariant measures, asymptotic behavior of typical orbits, ergodicity, mixing, decay of corre This volume serves a two-fold purpose: first, it gives a useful gateway to smooth ergodic theory for students and nonspecialists, and second, it provides a state-of-the-art report on important current aspects of the subject. The book is divided into three parts: lecture notes consisting of three long expositions with proofs aimed to serve as a comprehensive and self-contained introduction to a particular area of smooth ergodic theory; thematic sections based on mini-courses or surveys held at the conference; and original contributions presented at the meeting or closely related to the topics that were discussed there.
Book Synopsis Lectures on Random Evolution by : Mark A. Pinsky
Download or read book Lectures on Random Evolution written by Mark A. Pinsky and published by World Scientific. This book was released on 1991 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random evolution denotes a class of stochastic processes which evolve according to a rule which varies in time according to jumps. This is in contrast to diffusion processes, which assume that the rule changes continuously with time. Random evolutions provide a very flexible language, having the advantage that they permit direct numerical simulation-which is not possible for a diffusion process. Furthermore, they allow connections with hyperbolic partial differential equations and the kinetic theory of gases, which is impossible within the domain of diffusion proceses. They also posses great geometric invariance, allowing formulation on an arbitrary Riemannian manifold. In the field of stochastic stability, random evolutions furnish some easily computable models in which to study the Lyapunov exponent and rotation numbers of oscillators under the influence of noise. This monograph presents the various aspects of random evolution in an accessible and interesting format which will appeal to a large scientific audience.
