MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint

Local attractor continuation of non-autonomously perturbed systems

Martin Kell


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.

Mar 17, 2011
Mar 21, 2011
MSC Codes:
37B55, 37B35, 37L15
local attractor, non-autonomous perturbation, bounded noise

Related publications

2011 Repository Open Access
Martin Kell

Local attractor continuation of non-autonomously perturbed systems