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| Author | : Pedro Duarte |
| Publisher | : Springer |
| Total Pages | : 271 |
| Release | : 2016-03-21 |
| Genre | : Mathematics |
| ISBN | : 9462391246 |
Download Lyapunov Exponents of Linear Cocycles Book in PDF, ePub and Kindle
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.
| Author | : Marcelo Viana |
| Publisher | : Cambridge University Press |
| Total Pages | : 217 |
| Release | : 2014-07-24 |
| Genre | : Mathematics |
| ISBN | : 1316062694 |
Download Lectures on Lyapunov Exponents Book in PDF, ePub and Kindle
The theory of Lyapunov exponents originated over a century ago in the study of the stability of solutions of differential equations. Written by one of the subject's leading authorities, this book is both an account of the classical theory, from a modern view, and an introduction to the significant developments relating the subject to dynamical systems, ergodic theory, mathematical physics and probability. It is based on the author's own graduate course and is reasonably self-contained with an extensive set of exercises provided at the end of each chapter. This book makes a welcome addition to the literature, serving as a graduate text and a valuable reference for researchers in the field.
| Author | : Ludwig Arnold |
| Publisher | : Springer |
| Total Pages | : 372 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 354046431X |
Download Lyapunov Exponents Book in PDF, ePub and Kindle
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.
| Author | : João Lopes Dias |
| Publisher | : Springer Nature |
| Total Pages | : 184 |
| Release | : 2023-11-29 |
| Genre | : Mathematics |
| ISBN | : 3031413164 |
Download New Trends in Lyapunov Exponents Book in PDF, ePub and Kindle
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.
| Author | : Ludwig Arnold |
| Publisher | : Lecture Notes in Mathematics |
| Total Pages | : 392 |
| Release | : 1986-03 |
| Genre | : Mathematics |
| ISBN | : |
Download Lyapunov Exponents Book in PDF, ePub and Kindle
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.
| Author | : Marcelo Viana |
| Publisher | : Cambridge University Press |
| Total Pages | : 217 |
| Release | : 2014-07-24 |
| Genre | : Mathematics |
| ISBN | : 1107081734 |
Download Lectures on Lyapunov Exponents Book in PDF, ePub and Kindle
Covers the fundamental aspects of the classical theory and introduces significant recent developments. Based on the author's graduate course.
| Author | : Luís Barreira |
| Publisher | : |
| Total Pages | : 273 |
| Release | : 2017 |
| Genre | : Dynamics |
| ISBN | : 9783319712628 |
Download Lyapunov Exponents Book in PDF, ePub and Kindle
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.
| Author | : Jean Bourgain |
| Publisher | : Princeton University Press |
| Total Pages | : 183 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 0691120986 |
Download Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158) Book in PDF, ePub and Kindle
This book presents an overview of recent developments in the area of localization for quasi-periodic lattice Schrödinger operators and the theory of quasi-periodicity in Hamiltonian evolution equations. The physical motivation of these models extends back to the works of Rudolph Peierls and Douglas R. Hofstadter, and the models themselves have been a focus of mathematical research for two decades. Jean Bourgain here sets forth the results and techniques that have been discovered in the last few years. He puts special emphasis on so-called "non-perturbative" methods and the important role of subharmonic function theory and semi-algebraic set methods. He describes various applications to the theory of differential equations and dynamical systems, in particular to the quantum kicked rotor and KAM theory for nonlinear Hamiltonian evolution equations. Intended primarily for graduate students and researchers in the general area of dynamical systems and mathematical physics, the book provides a coherent account of a large body of work that is presently scattered in the literature. It does so in a refreshingly contained manner that seeks to convey the present technological "state of the art."
| Author | : Danijela Damjanovic |
| Publisher | : Cambridge University Press |
| Total Pages | : 446 |
| Release | : 2023-12-31 |
| Genre | : Mathematics |
| ISBN | : 1009278878 |
Download A Vision for Dynamics in the 21st Century Book in PDF, ePub and Kindle
A large international conference celebrated the 50-year career of Anatole Katok and the body of research across smooth dynamics and ergodic theory that he touched. In this book many leading experts provide an account of the latest developments at the research frontier and together set an agenda for future work, including an explicit problem list. This includes elliptic, parabolic, and hyperbolic smooth dynamics, ergodic theory, smooth ergodic theory, and actions of higher-rank groups. The chapters are written in a readable style and give a broad view of each topic; they blend the most current results with the developments leading up to them, and give a perspective on future work. This book is ideal for graduate students, instructors and researchers across all research areas in dynamical systems and related subjects.
| Author | : Christian Bonatti |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 390 |
| Release | : 2006-03-30 |
| Genre | : Mathematics |
| ISBN | : 3540268448 |
Download Dynamics Beyond Uniform Hyperbolicity Book in PDF, ePub and Kindle
What is Dynamics about? In broad terms, the goal of Dynamics is to describe the long term evolution of systems for which an "infinitesimal" evolution rule is known. Examples and applications arise from all branches of science and technology, like physics, chemistry, economics, ecology, communications, biology, computer science, or meteorology, to mention just a few. These systems have in common the fact that each possible state may be described by a finite (or infinite) number of observable quantities, like position, velocity, temperature, concentration, population density, and the like. Thus, m the space of states (phase space) is a subset M of an Euclidean space M . Usually, there are some constraints between these quantities: for instance, for ideal gases pressure times volume must be proportional to temperature. Then the space M is often a manifold, an n-dimensional surface for some n
