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035   $a(DE-He213)978-3-540-85964-2
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100   $a20100301d2009      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aLocal Lyapunov Exponents$b[electronic resource] $eSublimiting Growth Rates of Linear Random Differential Equations /$fby Wolfgang Siegert
205   $a1st ed. 2009.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2009.
215   $a1 online resource (IX, 254 p.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1963
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-540-85963-2 
320   $aIncludes bibliographical references (p. 239-251) and index.
327   $aLinear 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.
330   $aEstablishing a new concept of local Lyapunov exponents the author brings together two separate theories, namely Lyapunov exponents and the theory of large deviations. Specifically, a linear differential system is considered which is controlled by a stochastic process that during a suitable noise-intensity-dependent time is trapped near one of its so-called metastable states. The local Lyapunov exponent is then introduced as the exponential growth rate of the linear system on this time scale. Unlike classical Lyapunov exponents, which involve a limit as time increases to infinity in a fixed system, here the system itself changes as the noise intensity converges, too.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1963
606   $aProbabilities
606   $aDynamics
606   $aErgodic theory
606   $aDifferential equations
606   $aGlobal analysis (Mathematics)
606   $aManifolds (Mathematics)
606   $aGame theory
606   $aBiomathematics
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
606   $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X
606   $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147
606   $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082
606   $aGame Theory, Economics, Social and Behav. Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13011
606   $aGenetics and Population Dynamics$3https://scigraph.springernature.com/ontologies/product-market-codes/M31010
615  0$aProbabilities.
615  0$aDynamics.
615  0$aErgodic theory.
615  0$aDifferential equations.
615  0$aGlobal analysis (Mathematics).
615  0$aManifolds (Mathematics).
615  0$aGame theory.
615  0$aBiomathematics.
615 14$aProbability Theory and Stochastic Processes.
615 24$aDynamical Systems and Ergodic Theory.
615 24$aOrdinary Differential Equations.
615 24$aGlobal Analysis and Analysis on Manifolds.
615 24$aGame Theory, Economics, Social and Behav. Sciences.
615 24$aGenetics and Population Dynamics.
676   $a515.35
686   $aMAT 606f$2stub
686   $aSI 850$2rvk
686   $a60F10$a60H10$a37H15$a34F04$a34C11$a58J35$a91B28$a37N10$a92D15$a92D25$2msc
700   $aSiegert$b Wolfgang$4aut$4http://id.loc.gov/vocabulary/relators/aut$0472379
906   $aBOOK
912   $a9910484132603321
996   $aLocal Lyapunov exponents$9230315
997   $aUNINA