Uniform nonautonomous attractors under discretization
P.E. Kloeden - FB Mathematik, Johann Wolfgang Goethe Universität, Postfach 11 19 32, D-60054 Frankfurt a.M., Germany (email)
Abstract: 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.
Keywords: Cocycle dynamical systems, attractors, perturbations, discretization.
Received: October 2001; Revised: February 2003; Available Online: October 2003.
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