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April  2005, 13(3): 827-841. doi: 10.3934/dcds.2005.13.827

Attractors under discretizations with variable stepsize

Barnabas M. Garay 1, and  Keonhee Lee 2,

1. 

Department of Mathematics, University of Technology, 1521 Budapest, Hungary
2. 

Department of Mathematics, Chungnam National University, Daejeon, 305-764

Received  January 2003 Revised  May 2005 Published  May 2005

The standard upper and lower semicontinuity results for discretized attractors [22], [13], [5] are generalized for discretizations with variable stepsize. Several examples demonstrate that the limiting behaviour depends crucially on the stepsize sequence. For stepsize sequences suitably chosen, convergence to the exact attractor in the Hausdorff metric is proven. Connections to pullback attractors in cocycle dynamics are pointed out.
Keywords: variable stepsize, discretization., Attractor.
Mathematics Subject Classification: Primary: 65L05; Secondary: 37B25, 34C3.
Citation: Barnabas M. Garay, Keonhee Lee. Attractors under discretizations with variable stepsize. Discrete & Continuous Dynamical Systems, 2005, 13 (3) : 827-841. doi: 10.3934/dcds.2005.13.827
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