04307nam 22008415 450 991048413260332120200705123858.03-540-85964-010.1007/978-3-540-85964-2(CKB)1000000000546286(SSID)ssj0000679709(PQKBManifestationID)11436933(PQKBTitleCode)TC0000679709(PQKBWorkID)10624617(PQKB)10703683(DE-He213)978-3-540-85964-2(MiAaPQ)EBC3063867(PPN)132868369(EXLCZ)99100000000054628620100301d2009 u| 0engurnn|008mamaatxtccrLocal Lyapunov Exponents Sublimiting Growth Rates of Linear Random Differential Equations /by Wolfgang Siegert1st ed. 2009.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2009.1 online resource (IX, 254 p.) Lecture Notes in Mathematics,0075-8434 ;1963Bibliographic Level Mode of Issuance: Monograph3-540-85963-2 Includes bibliographical references (p. 239-251) and index.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.Lecture Notes in Mathematics,0075-8434 ;1963ProbabilitiesDynamicsErgodic theoryDifferential equationsGlobal analysis (Mathematics)Manifolds (Mathematics)Game theoryBiomathematicsProbability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Dynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XOrdinary Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12147Global Analysis and Analysis on Manifoldshttps://scigraph.springernature.com/ontologies/product-market-codes/M12082Game Theory, Economics, Social and Behav. Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/M13011Genetics and Population Dynamicshttps://scigraph.springernature.com/ontologies/product-market-codes/M31010Probabilities.Dynamics.Ergodic theory.Differential equations.Global analysis (Mathematics).Manifolds (Mathematics).Game theory.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.515.35MAT 606fstubSI 850rvk60F1060H1037H1534F0434C1158J3591B2837N1092D1592D25mscSiegert Wolfgangauthttp://id.loc.gov/vocabulary/relators/aut472379BOOK9910484132603321Local Lyapunov exponents230315UNINA