Overview
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.
Full Product Details
Author: Wolfgang Siegert
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition: 2009 ed.
Volume: 1963
Dimensions:
Width: 15.50cm
, Height: 1.40cm
, Length: 23.50cm
Weight: 0.454kg
ISBN: 9783540859635
ISBN 10: 3540859632
Pages: 254
Publication Date: 13 November 2008
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: In Print
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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 Hogele, Zentralblatt MATH, Vol. 1178, 2010)
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 Hogele, Zentralblatt MATH, Vol. 1178, 2010)
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 Hogele, Zentralblatt MATH, Vol. 1178, 2010)
