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New Trends In Lyapunov Exponents


New Trends In Lyapunov Exponents
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New Trends In Lyapunov Exponents


New Trends In Lyapunov Exponents
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Author : João Lopes Dias
language : en
Publisher: Springer Nature
Release Date : 2023-11-29

New Trends In Lyapunov Exponents written by João Lopes Dias and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-29 with Mathematics categories.


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.



Lectures On Lyapunov Exponents


Lectures On Lyapunov Exponents
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Author : Marcelo Viana
language : en
Publisher: Cambridge University Press
Release Date : 2014-07-24

Lectures On Lyapunov Exponents written by Marcelo Viana 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 2014-07-24 with Mathematics categories.


Covers the fundamental aspects of the classical theory and introduces significant recent developments. Based on the author's graduate course.



Lyapunov Exponents


Lyapunov Exponents
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Author : Luís Barreira
language : en
Publisher: Birkhäuser
Release Date : 2017-12-30

Lyapunov Exponents written by Luís Barreira and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-30 with Mathematics categories.


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.



Lyapunov Exponents


Lyapunov Exponents
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Author : Ludwig Arnold
language : en
Publisher: Springer
Release Date : 2006-11-14

Lyapunov Exponents written by Ludwig Arnold and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.


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.



New Trends In Information And Communications Technology Applications


New Trends In Information And Communications Technology Applications
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Author : Abbas M. Al-Bakry
language : en
Publisher: Springer Nature
Release Date :

New Trends In Information And Communications Technology Applications written by Abbas M. Al-Bakry and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.




Local Lyapunov Exponents


Local Lyapunov Exponents
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Author : Wolfgang Siegert
language : en
Publisher: Springer Science & Business Media
Release Date : 2009

Local Lyapunov Exponents written by Wolfgang Siegert 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 2009 with Mathematics categories.


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.



Lyapunov Exponents


Lyapunov Exponents
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Author : Ludwig Arnold
language : en
Publisher:
Release Date : 1986

Lyapunov Exponents written by Ludwig Arnold and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.




New Trends In Turbulence Turbulence Nouveaux Aspects


New Trends In Turbulence Turbulence Nouveaux Aspects
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Author : M. Lesieur
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-01

New Trends In Turbulence Turbulence Nouveaux Aspects written by M. Lesieur 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 2003-07-01 with Science categories.


Following a longstanding tradition of the Les Houches Summer Schools, this book uses a pedagogically presented and accessible style to treat 2D and 3D turbulence from the experimental, theoretical and computational points of view.



Predictability Of Chaotic Dynamics


Predictability Of Chaotic Dynamics
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Author : Juan C. Vallejo
language : en
Publisher: Springer
Release Date : 2017-03-27

Predictability Of Chaotic Dynamics written by Juan C. Vallejo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-27 with Science categories.


This book is primarily concerned with the computational aspects of predictability of dynamical systems – in particular those where observation, modeling and computation are strongly interdependent. Unlike with physical systems under control in laboratories, for instance in celestial mechanics, one is confronted with the observation and modeling of systems without the possibility of altering the key parameters of the objects studied. Therefore, the numerical simulations offer an essential tool for analyzing these systems. With the widespread use of computer simulations to solve complex dynamical systems, the reliability of the numerical calculations is of ever-increasing interest and importance. This reliability is directly related to the regularity and instability properties of the modeled flow. In this interdisciplinary scenario, the underlying physics provide the simulated models, nonlinear dynamics provides their chaoticity and instability properties, and the computer sciences provide the actual numerical implementation. This book introduces and explores precisely this link between the models and their predictability characterization based on concepts derived from the field of nonlinear dynamics, with a focus on the finite-time Lyapunov exponents approach. The method is illustrated using a number of well-known continuous dynamical systems, including the Contopoulos, Hénon-Heiles and Rössler systems. To help students and newcomers quickly learn to apply these techniques, the appendix provides descriptions of the algorithms used throughout the text and details how to implement them in order to solve a given continuous dynamical system.



Local Lyapunov Exponents


Local Lyapunov Exponents
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Author : Wolfgang Siegert
language : en
Publisher: Springer
Release Date : 2008-11-13

Local Lyapunov Exponents written by Wolfgang Siegert and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-13 with Mathematics categories.


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.