Affordable Access

Synchronisation of almost all trajectories of a random dynamical system

Authors
  • Newman, Julian
Type
Preprint
Publication Date
Jan 09, 2016
Submission Date
Nov 27, 2015
Identifiers
arXiv ID: 1511.08831
Source
arXiv
License
Yellow
External links

Abstract

It has been shown by Le Jan that, given a memoryless-noise random dynamical system together with an ergodic distribution for the associated Markov transition probabilities, if the support of the ergodic distribution admits locally asymptotically stable trajectories, then there is a random attracting set consisting of finitely many points, whose basin of forward-time attraction includes a random full measure open set. In this paper, we present necessary and sufficient conditions for this attracting set to be a singleton; our result does not require the state space to be compact, but holds on general Lusin metric spaces.

Report this publication

Statistics

Seen <100 times