Local Lyapunov exponents: Sublimiting growth rates of linear random differential equations

Wolfgang Siegert (auth.)3540859632

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.

Table of contents :
Front Matter….Pages i-xvi
Linear differential systems with parameter excitation….Pages 9-51
Locality and time scales of the underlying non-degenerate stochastic system: Freidlin-Wentzell theory….Pages 53-123
Exit probabilities for degenerate systems….Pages 125-142
Local Lyapunov exponents….Pages 143-229
Back Matter….Pages 231-260