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- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1963)
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About this book
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.
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Table of contents (4 chapters)
Reviews
From the reviews:
“These lecture notes originate from the author's dissertation and provide a self-contained introduction to the notion of local Lyapunov exponents. … provide a beautiful exposition to this partially subtle subject for readers acquainted with the theory of stochastic differential equations. … Great qualities of this book are also the ample bibliography giving a representative state of the large literature in this field and the great amount of instructively worked out examples. … The composition of the text is throughout clear, carefully thought through and harmonic.” (Michael Högele, Zentralblatt MATH, Vol. 1178, 2010)Authors and Affiliations
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Bibliographic Information
Book Title: Local Lyapunov Exponents
Book Subtitle: Sublimiting Growth Rates of Linear Random Differential Equations
Authors: Wolfgang Siegert
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-540-85964-2
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2009
Softcover ISBN: 978-3-540-85963-5Published: 13 November 2008
eBook ISBN: 978-3-540-85964-2Published: 17 December 2008
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: IX, 254
Topics: Probability Theory and Stochastic Processes, Dynamical Systems and Ergodic Theory, Ordinary Differential Equations, Global Analysis and Analysis on Manifolds, Game Theory, Economics, Social and Behav. Sciences, Genetics and Population Dynamics