LEADER 02791nam 2200613Ia 450 001 9910484132603321 005 20200520144314.0 010 $a9783540859642 010 $a3540859640 024 7 $a10.1007/978-3-540-85964-2 035 $a(CKB)1000000000546286 035 $a(SSID)ssj0000679709 035 $a(PQKBManifestationID)11436933 035 $a(PQKBTitleCode)TC0000679709 035 $a(PQKBWorkID)10624617 035 $a(PQKB)10703683 035 $a(DE-He213)978-3-540-85964-2 035 $a(MiAaPQ)EBC3063867 035 $a(PPN)132868369 035 $a(EXLCZ)991000000000546286 100 $a20081103d2009 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aLocal Lyapunov exponents $esublimiting growth rates of linear random differential equations /$fWolfgang Siegert 205 $a1st ed. 2009. 210 $aBerlin $cSpringer$d2009 215 $a1 online resource (IX, 254 p.) 225 1 $aLecture notes in mathematics ;$v1963 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9783540859635 311 08$a3540859632 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 (Springer-Verlag) ;$v1963. 606 $aLyapunov exponents 606 $aDifferential equations 615 0$aLyapunov exponents. 615 0$aDifferential equations. 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$0472379 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484132603321 996 $aLocal Lyapunov exponents$9230315 997 $aUNINA