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MiS Preprint
97/2020

Random attractors for dissipative systems with rough noises

Hoang Duc Luu

Abstract

We provide an analytic approach to study the asymptotic dynamics of rough differential equations, with the driving noises of H\"older continuity. Such systems can be solved with Lyons' theory of rough paths, in particular the rough integrals are understood in the Gubinelli sense for controlled rough paths. Using the framework of random dynamical systems and random attractors, we prove the existence and upper semi-continuity of the global pullback attractor for dissipative systems perturbed by bounded noises. Moreover, if the unperturbed system is strictly dissipative then the random attractor is a singleton for sufficiently small noise intensity.

Received:
06.10.2020
Published:
06.10.2020

Related publications

inJournal
2022 Repository Open Access
Hoang Duc Luu

Random attractors for dissipative systems with rough noises

In: Discrete and continuous dynamical systems / A, 42 (2022) 4, pp. 1873-1902