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010   $a3-319-61934-9
024 7 $a10.1007/978-3-319-61934-7
035   $a(CKB)3710000001631065
035   $a(MiAaPQ)EBC4946532
035   $a(DE-He213)978-3-319-61934-7
035   $a(PPN)20385179X
035   $a(EXLCZ)993710000001631065
100   $a20170811d2017      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $2rdacontent
182   $2rdamedia
183   $2rdacarrier
200 10$aAttractors under discretisation /$fby Xiaoying Han, Peter Kloeden
205   $a1st ed. 2017.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017.
215   $a1 online resource (121 pages)
225 1 $aSpringerBriefs in Mathematics,$x2191-8198
311 08$a3-319-61933-0 
327   $aPart I Dynamical systems and numerical schemes -- 1 Lyapunov stability and dynamical systems -- 2 One step numerical schemes -- Part II Steady states under discretization -- 3 Linear systems -- 4 Lyapunov functions -- 5 Dissipative systems with steady states -- 6 Saddle points under discretisation . Part III Autonomous attractors under discretization -- 7 Dissipative systems with attractors -- 8 Lyapunov functions for attractors -- 9 Discretisation of an attractor. Part IV Nonautonomous limit sets under discretization -- 10 Dissipative nonautonomous systems  -- 11 Discretisation of nonautonomous limit sets -- 12 Variable step size -- 13 Discretisation of a uniform pullback attractor -- Notes -- References.
330   $aThis work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained ? by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size were considered, so the resulting discrete time dynamical system was also autonomous. One of the aims of this book is to present new findings on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, and in particular to examine the properties of nonautonomous omega limit sets and their approximations by numerical schemes ? results that are also of importance for autonomous systems approximated by a numerical scheme with variable time steps, thus by a discrete time nonautonomous dynamical system.
410  0$aSpringerBriefs in Mathematics,$x2191-8198
606   $aNumerical analysis
606   $aDynamics
606   $aErgodic theory
606   $aDifferential equations
606   $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050
606   $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X
606   $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147
615  0$aNumerical analysis.
615  0$aDynamics.
615  0$aErgodic theory.
615  0$aDifferential equations.
615 14$aNumerical Analysis.
615 24$aDynamical Systems and Ergodic Theory.
615 24$aOrdinary Differential Equations.
676   $a514.74
700   $aHan$b Xiaoying$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755831
702   $aKloeden$b Peter$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910254302003321
996   $aAttractors Under Discretisation$92179913
997   $aUNINA