# American Institute of Mathematical Sciences

February  2004, 10(1&2): 423-433. doi: 10.3934/dcds.2004.10.423

## Uniform nonautonomous attractors under discretization

 1 FB Mathematik, Johann Wolfgang Goethe Universität, Postfach 11 19 32, D-60054 Frankfurt a.M., Germany 2 Institute for Information Transmission Problems, Russian Academy of Sciences, Bolshoj Karetny lane, 19, 101447 Moscow, Russian Federation

Received  October 2001 Revised  February 2003 Published  October 2003

A nonautonomous or cocycle dynamical system that is driven by an autonomous dynamical system acting on a compact metric space is assumed to have a uniform pullback attractor. It is shown that discretization by a one-step numerical scheme gives rise to a discrete time cocycle dynamical system with a uniform pullback attractor, the component subsets of which converge upper semi continuously to their continuous time counterparts as the maximum time step decreases to zero. The proof involves a Lyapunov function characterizing the uniform pullback attractor of the original system.
Citation: P.E. Kloeden, Victor S. Kozyakin. Uniform nonautonomous attractors under discretization. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 423-433. doi: 10.3934/dcds.2004.10.423
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