LEADER 03128nam 2200589 450 001 996466613203316 005 20220224161928.0 010 $a3-540-48429-9 024 7 $a10.1007/BFb0093184 035 $a(CKB)1000000000437306 035 $a(SSID)ssj0000326640 035 $a(PQKBManifestationID)12069598 035 $a(PQKBTitleCode)TC0000326640 035 $a(PQKBWorkID)10296693 035 $a(PQKB)10668809 035 $a(DE-He213)978-3-540-48429-5 035 $a(MiAaPQ)EBC5578117 035 $a(Au-PeEL)EBL5578117 035 $a(OCoLC)1066178725 035 $a(MiAaPQ)EBC6858024 035 $a(Au-PeEL)EBL6858024 035 $a(PPN)155210394 035 $a(EXLCZ)991000000000437306 100 $a20220224d1999 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aShadowing in dynamical systems /$fSergei Yu. Pilyugin 205 $a1st ed. 1999. 210 1$aBerlin :$cSpringer,$d[1999] 210 4$dİ1999 215 $a1 online resource (XX, 276 p.) 225 0 $aLecture notes in mathematics ;$v1706 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-66299-5 327 $aShadowing Near an Invariant Set: Basic Definitions. Shadowing Near a Hyperbolic Set for a Diffeomorphism. Shadowing for Mappings of Banach Spaces. Limit Shadowing. Shadowing for Flows -- Topologically Stable, Structurally Stable, and Generic Systems: Shadowing and Topological Stability. Shadowing in Structurally Stable Systems. Shadowing in Two-Dimensional Diffeomorphisms. C0-Genericity of Shadowing for Homeomorphisms -- Systems with Special Structure: One-Dimensional Systems. Linear and Linearly Induced Systems. Lattice Systems. Global Attractors for Evolution Systems -- Numerical Applications of Shadowing: Finite Shadowing. Periodic Shadowing for Flows. Approximation of Spectral Characteristics. Approximation of the Morse Spectrum. Discretizations of PDEs -- References -- Index. 330 $aThis book is an introduction to the theory of shadowing of approximate trajectories in dynamical systems by exact ones. This is the first book completely devoted to the theory of shadowing. It shows the importance of shadowing theory for both the qualitative theory of dynamical systems and the theory of numerical methods. Shadowing Methods allow us to estimate differences between exact and approximate solutions on infinite time intervals and to understand the influence of error terms. The book is intended for specialists in dynamical systems, for researchers and graduate students in the theory of numerical methods. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1706 606 $aDifferentiable dynamical systems 615 0$aDifferentiable dynamical systems. 676 $a515.352 686 $a37C50$2msc 700 $aPilyugin$b Sergei Yu$g(Sergei Yurievitch),$f1947-$060268 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466613203316 996 $aShadowing in dynamical systems$9262404 997 $aUNISA