Uniform nonautonomous attractors under discretization

P.E. Kloeden; Victor S. Kozyakin

doi:10.3934/dcds.2004.10.423

Article Contents

2004, Volume 10, Issue 1&2: 423-433. Doi: 10.3934/dcds.2004.10.423

This issue Previous Article On the free boundary regularity theorem of Alt and Caffarelli Next Article On a limiting system in the Lotka--Volterra competition with cross-diffusion

Uniform nonautonomous attractors under discretization

P.E. Kloeden^1, and
Victor S. Kozyakin^2,

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

Received: September 30, 2001

Revised: January 31, 2003

Published: December 2003

Abstract Related Papers Cited by

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:

Mathematics Subject Classification: 34D10, 34D45, 37C60.

Citation:

Article Metrics

HTML views() PDF downloads(37) Cited by(0)

Uniform nonautonomous attractors under discretization

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Uniform nonautonomous attractors under discretization

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content