Ebook: Local Lyapunov exponents: Sublimiting growth rates of linear random differential equations
Author: Wolfgang Siegert (auth.)
- Genre: Mathematics
- Tags: Dynamical Systems and Ergodic Theory, Global Analysis and Analysis on Manifolds, Ordinary Differential Equations, Partial Differential Equations, Game Theory Economics Social and Behav. Sciences, Genetics and Population Dynamics
- Series: Lecture Notes in Mathematics 1963
- Year: 2009
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
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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.
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.