Local attractor continuation of non-autonomously perturbed systems

Martin Kell

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Submission date: 17. Mar. 2011
Pages: 17
Bibtex
MSC-Numbers: 37B55, 37B35, 37L15
Keywords and phrases: local attractor, non-autonomous perturbation, bounded noise
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Abstract:
Using Conley theory we show that local attractors remain (past) attractors under small non-autonomous perturbations. In particular, the attractors of the perturbed systems will have positive invariant neighborhoods and converge upper semicontinuously to the original attractor.
The result is split into a finite-dimensional part (locally compact) and an infinite-dimensional part (not necessarily locally compact). The finite-dimensional part will be applicable to bounded random noise, i.e. continuous time random dynamical systems on a locally compact metric space which are uniformly close the unperturbed deterministic system. The “closeness” will be defined via a (simpler version of) convergence coming from singular perturbations theory.