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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.

Lyapunov exponents --- Differential equations --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Applied Mathematics --- Mathematical Theory --- Lyapunov exponents. --- Differential equations. --- 517.91 Differential equations --- Liapunov exponents --- Lyapunov characteristic exponents --- Mathematics. --- Dynamics. --- Ergodic theory. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Game theory. --- Probabilities. --- Biomathematics. --- 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. --- Biology --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Games, Theory of --- Theory of games --- Mathematical models --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Math --- Science --- Distribution (Probability theory. --- Differentiable dynamical systems. --- Differential Equations. --- Global analysis. --- Genetics --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Heredity --- Mutation (Biology) --- Variation (Biology) --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities

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Differential geometry. Global analysis --- Ergodic theory. Information theory --- Partial differential equations --- Differential equations --- Operational research. Game theory --- Genetics --- differentiaalvergelijkingen --- differentiaal geometrie --- genetica --- speltheorie --- informatietheorie