Lecture Notes in Mathematics

Local Lyapunov Exponents

Sublimiting Growth Rates of Linear Random Differential Equations

Authors: Siegert, Wolfgang

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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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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)

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook 42,79 €
price for Spain (gross)
  • ISBN 978-3-540-85964-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Softcover 51,99 €
price for Spain (gross)
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Bibliographic Information

Bibliographic Information
Book Title
Local Lyapunov Exponents
Book Subtitle
Sublimiting Growth Rates of Linear Random Differential Equations
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1963
Copyright
2009
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-85964-2
DOI
10.1007/978-3-540-85964-2
Softcover ISBN
978-3-540-85963-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
IX, 254
Topics