Local Lyapunov Exponents [electronic resource] : Sublimiting Growth Rates of Linear Random Differential Equations / by Wolfgang Siegert.
Material type: TextSeries: Lecture Notes in Mathematics ; 1963Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009Description: IX, 254 p. online resourceContent type:- text
- computer
- online resource
- 9783540859642
- Distribution (Probability theory
- Differentiable dynamical systems
- Differential Equations
- Global analysis
- Mathematics
- Genetics -- Mathematics
- Probability Theory and Stochastic Processes
- Dynamical Systems and Ergodic Theory
- Ordinary Differential Equations
- Global Analysis and Analysis on Manifolds
- Game Theory, Economics, Social and Behav. Sciences
- Genetics and Population Dynamics
- 519.2 23
- QA273.A1-274.9
- QA274-274.9
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.
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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