TY - BOOK ID - 14296013 TI - Local Lyapunov exponents : sublimiting growth rates of linear random differential equations PY - 2009 SN - 3540859632 3540859640 PB - Berlin : Springer, DB - UniCat KW - Lyapunov exponents KW - Differential equations KW - Engineering & Applied Sciences KW - Mathematics KW - Physical Sciences & Mathematics KW - Calculus KW - Applied Mathematics KW - Mathematical Theory KW - Lyapunov exponents. KW - Differential equations. KW - 517.91 Differential equations KW - Liapunov exponents KW - Lyapunov characteristic exponents KW - Mathematics. KW - Dynamics. KW - Ergodic theory. KW - Global analysis (Mathematics). KW - Manifolds (Mathematics). KW - Game theory. KW - Probabilities. KW - Biomathematics. KW - Probability Theory and Stochastic Processes. KW - Dynamical Systems and Ergodic Theory. KW - Ordinary Differential Equations. KW - Global Analysis and Analysis on Manifolds. KW - Game Theory, Economics, Social and Behav. Sciences. KW - Genetics and Population Dynamics. KW - Biology KW - Probability KW - Statistical inference KW - Combinations KW - Chance KW - Least squares KW - Mathematical statistics KW - Risk KW - Games, Theory of KW - Theory of games KW - Mathematical models KW - Geometry, Differential KW - Topology KW - Analysis, Global (Mathematics) KW - Differential topology KW - Functions of complex variables KW - Geometry, Algebraic KW - Ergodic transformations KW - Continuous groups KW - Mathematical physics KW - Measure theory KW - Transformations (Mathematics) KW - Dynamical systems KW - Kinetics KW - Mechanics, Analytic KW - Force and energy KW - Mechanics KW - Physics KW - Statics KW - Math KW - Science KW - Distribution (Probability theory. KW - Differentiable dynamical systems. KW - Differential Equations. KW - Global analysis. KW - Genetics KW - Embryology KW - Mendel's law KW - Adaptation (Biology) KW - Breeding KW - Chromosomes KW - Heredity KW - Mutation (Biology) KW - Variation (Biology) KW - Differential dynamical systems KW - Dynamical systems, Differentiable KW - Dynamics, Differentiable KW - Global analysis (Mathematics) KW - Topological dynamics KW - Distribution functions KW - Frequency distribution KW - Characteristic functions KW - Probabilities UR - https://www.unicat.be/uniCat?func=search&query=sysid:14296013 AB - 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. ER -