Attractors under discretizations with variable stepsize | Zendy

Barnabás M. Garay | Zendy; Keonhee Lee | Zendy

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Attractors under discretizations with variable stepsize

Author(s) -

Barnabás M. Garay,

Keonhee Lee

Publication year - 2005

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2005.13.827

Subject(s) - pullback attractor , attractor , hausdorff distance , mathematics , sequence (biology) , hausdorff space , variable (mathematics) , limiting , convergence (economics) , mathematical analysis , pure mathematics , mechanical engineering , genetics , engineering , economics , biology , economic growth

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 Hausdorfi metric is proven. Connections to pullback attractors in cocycle dynamics are pointed out.

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