Titlebook: Attractors Under Discretisation; Xiaoying Han,Peter Kloeden Book 2017 The Author(s) 2017 One step numerical schemes.Autonomous dynamicl sy

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Produktdesign: Materialeigenschaften,Saddle points for Euler schemes for ODEs are discussed. Numerical stable and unstable manifolds are illustrated through a set of examples, and compared to the stable and unstable manifolds of the ODEs. The shadowing phenomenon is briefly illustrated. Finally, Beyn’s Theorem is presented.

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Ram K. Mishra,Glen B. Baker,Alan A. BoultonEuler schemes for dissipative ODE systems with attractors are presented and shown to possess numerical attractors that converge to the ODE attractors upper semi continuously. A counterexample shows that the numerical attractor need not convergence lower semi continuously.

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Stephanie J. Walker,H. Alex BrownNonautonomous dynamical systems and their omega limit sets are defined. The concepts of positive and negative asymptotic invariance are defined. The omega limit sets for dissipative nonautonomous dynamical systems are shown to be positive and negative asymptotic invariant under certain conditions.

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https://doi.org/10.1385/1592594301Numerical nonautonomous omega limit sets for nonautonomous ODEs are constructed by using the implicit Euler scheme and shown to converge to the omega limit sets for the ODEs upper semi continuously.

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Patricia M. Hinkle,John A. PuskasPullback and forward attractors for skew product flows are introduced, then the implicit Euler numerical scheme is applied to obtain a discrete time skew product flow. Existence of a numerical attractor for this discrete time skew product flow is established for sufficiently small step size.

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