Local Lyapunov Exponents Sublimiting Growth Rates of Linear Random Differential Equations /

• Main Author: Siegert, Wolfgang. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Lecture Notes in Mathematics, 1963
• Subjects: Mathematics.; Differentiable dynamical systems.; Global analysis.; Differential Equations.; Differential equations, partial.; Genetics > Mathematics.; 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.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-540-85964-2
• Physical Description: IX, 254 p. online resource.
• ISBN: 9783540859642
• ISSN: 0075-8434

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.