Local Lyapunov Exponents (eBook)

Sublimiting Growth Rates of Linear Random Differential Equations

Wolfgang Siegert (Autor)

eBook Download: PDF

2008 | 2009
IX, 254 Seiten
Springer Berlin (Verlag)
978-3-540-85964-2 (ISBN)

Infos

Establishing a new concept of local Lyapunov exponents, this volume brings together two separate theories, namely Lyapunov exponents and the theory of large deviations.

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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.

Inhalt

Linear differential systems with parameter excitation.- Locality and time scales of the underlying non-degenerate stochastic system: Freidlin-Wentzell theory.- Exit probabilities for degenerate systems.- Local Lyapunov exponents.

Produkt-Details

• Erscheint lt. Verlag: 17.12.2008
• Reihe/Serie: Lecture Notes in Mathematics
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Schlagworte: 60F10, 60H10, 37H15, 34F05, 34C11, 58J35, 91B28, 37N10, 92D1 • degenerate diffusion • exit probabilities • metastability • random perturbations of dynamical systems • Stochastic process • sublimiting exponential growth rate
• ISBN-10: 3-540-85964-0 / 3540859640
• ISBN-13: 978-3-540-85964-2 / 9783540859642