Lyapunov Exponents Of Linear Cocycles
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| Author | : Pedro Duarte |
| Publisher | : Springer |
| Total Pages | : 271 |
| Release | : 2016-03-21 |
| Genre | : Mathematics |
| ISBN | : 9462391246 |
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 |
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 | : Sirakov Boyan |
| Publisher | : World Scientific |
| Total Pages | : 5396 |
| Release | : 2019-02-27 |
| Genre | : Mathematics |
| ISBN | : 9813272899 |
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
| Author | : Luis Barreira |
| Publisher | : |
| Total Pages | : |
| Release | : 2014-02-19 |
| Genre | : |
| ISBN | : 9781299707306 |
A self-contained, comprehensive account of modern smooth ergodic theory, the mathematical foundation of deterministic chaos.
| Author | : Marcelo Viana |
| Publisher | : Cambridge University Press |
| Total Pages | : 217 |
| Release | : 2014-07-24 |
| Genre | : Mathematics |
| ISBN | : 1107081734 |
Covers the fundamental aspects of the classical theory and introduces significant recent developments. Based on the author's graduate course.
| Author | : João Lopes Dias |
| Publisher | : Springer Nature |
| Total Pages | : 184 |
| Release | : 2023-11-29 |
| Genre | : Mathematics |
| ISBN | : 3031413164 |
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 | : Mark Pollicott |
| Publisher | : Cambridge University Press |
| Total Pages | : 176 |
| Release | : 1993-02-04 |
| Genre | : Mathematics |
| ISBN | : 9780521435932 |
These lecture notes provide a unique introduction to Pesin theory and its applications.
| Author | : Ludwig Arnold |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 590 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 3662128780 |
The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.
| Author | : Danijela Damjanovic |
| Publisher | : Cambridge University Press |
| Total Pages | : 446 |
| Release | : 2023-12-31 |
| Genre | : Mathematics |
| ISBN | : 1009278878 |
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 |
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
