Journal of the Korean Mathematical Society, ( ISI ), Volume (60), No (2), Year (2023-3) , Pages (255-271)

Title : ( INVARIANT GRAPH AND RANDOM BONY ATTRACTORS )

Authors: Fateme Helen Ghane Ostadghassemi , Maryam Rabiee Farahani , marzie zaj ,

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Abstract

In this paper, we deal with random attractors for dynamical systems forced by a deterministic noise. These kind of systems are modeled as skew products where the dynamics of the forcing process are described by the base transformation. Here, we consider skew products over the Bernoulli shift with the unit interval fiber. We study the geometric structure of maximal attractors, the orbit stability and stability of mixing of these skew products under random perturbations of the fiber maps. We show that there exists an open set U in the space of such skew products so that any skew product belonging to this set admits an attractor which is either a continuous invariant graph or a bony graph attractor. These skew products have negative fiber Lyapunov exponents and their fiber maps are non-uniformly contracting, hence the non-uniform contraction rates are measured by Lyapnnov exponents. Furthermore, each skew product of U admits an invariant ergodic measure whose support is contained in that attractor. Additionally, we show that the invariant measure for the perturbed system is continuous in the Hutchinson metric.

Keywords

, Skew products, maximal attractor, invariant graph, bony attractor
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@article{paperid:1094779,
author = {Ghane Ostadghassemi, Fateme Helen and Rabiee Farahani, Maryam and Zaj, Marzie},
title = {INVARIANT GRAPH AND RANDOM BONY ATTRACTORS},
journal = {Journal of the Korean Mathematical Society},
year = {2023},
volume = {60},
number = {2},
month = {March},
issn = {0304-9914},
pages = {255--271},
numpages = {16},
keywords = {Skew products; maximal attractor; invariant graph; bony attractor},
}

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%0 Journal Article
%T INVARIANT GRAPH AND RANDOM BONY ATTRACTORS
%A Ghane Ostadghassemi, Fateme Helen
%A Rabiee Farahani, Maryam
%A Zaj, Marzie
%J Journal of the Korean Mathematical Society
%@ 0304-9914
%D 2023

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