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 Media type: computer Carrier type: online resourceISBN: 9783540859642Subject(s): Mathematics | Differentiable dynamical systems | Global analysis | Differential Equations | Differential equations, partial | Genetics -- Mathematics | 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 DynamicsAdditional physical formats: Printed edition:: No titleDDC classification: 515.39 | 515.48 LOC classification: QA313Online resources: Click here to access onlineCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK1904 |
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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