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MiS Preprint
71/2013

A family of rotation numbers for discrete random dynamics on the circle

Christian S. Rodrigues and Paulo R. C. Ruffino

Abstract

We revisit the problem of well-defining rotation numbers for discrete random dynamical systems on $S^1$. We show that, contrasting with deterministic systems, the topological (i.e. based on Poincaré lifts) approach does depend on the choice of lifts (e.g. continuously for nonatomic randomness). Furthermore, the winding orbit rotation number does not agree with the topological rotation number. Existence and conversion formulae between these distinct numbers are presented. Finally, we prove a sampling in time theorem which recover the rotation number of continuous Stratonovich stochastic dynamical systems on $S^1$ out of its time discretisation of the flow.

Received:
Jul 19, 2013
Published:
Jul 19, 2013
MSC Codes:
37C40, 37E45, 37E10, 37A05

Related publications

inJournal
2015 Repository Open Access
Christian S. Rodrigues and Paulo R. C. Ruffino

A family of rotation numbers for discrete random dynamics on the circle

In: Stochastics and dynamics, 15 (2015) 3, p. 1550021