Lyapunov functions and attractors under variable time-step discretization

DOI10.3934/dcds.1996.2.163zbMath0949.34042OpenAlexW1964078443MaRDI QIDQ1576684

Peter E. Kloeden, Björn Schmalfuss

Publication date: 16 August 2000

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.1996.2.163

zbMATH Keywords

Lyapunov functioncocycle attractornonautonomous difference equationHausdorff separationassociated discrete time cocycleequivariant sets

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Attractors of solutions to ordinary differential equations (34D45) Computational methods for bifurcation problems in dynamical systems (37M20)

Related Items (10)

A Lyapunov-Type Theorem for Dissipative Numerical Integrators with Adaptive Time-Stepping ⋮ Summability characterizations of uniform exponential and asymptotic stability of sets for difference inclusions ⋮ Asymptotic behaviour of nonautonomous difference inclusions ⋮ Input-to-state stability, numerical dynamics and sampled-data control ⋮ Nonautonomous and random attractors ⋮ The inflated attractors of non-autonomous strongly damped wave equations ⋮ Upper semicontinuous dependence of pullback attractors on time scales ⋮ The inflation of attractors and their discretization: The autonomous case ⋮ Pullback attractors in nonautonomous difference equations ⋮ The relation between the existence of bounded solutions of differential equations and the corresponding difference equations

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