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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Rodrigues, Christian S. [1] ; Ruffino, Paulo R. C. [2]
Total Authors: 2
[1] Max Planck Inst Math Sci, D-04103 Leipzig - Germany
[2] Univ Estadual Campinas, Dept Matemat, BR-13 08385 Campinas, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Stochastics and Dynamics; v. 15, n. 3 SEP 2015.
Web of Science Citations: 0

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 Poincare 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 recovers the rotation number of continuous Stratonovich stochastic dynamical systems on S-1 out of its time discretization of the flow. (AU)

FAPESP's process: 11/50151-0 - Dynamical phenomena in complex networks: fundamentals and applications
Grantee:Elbert Einstein Nehrer Macau
Support type: Research Projects - Thematic Grants
FAPESP's process: 12/18780-0 - Geometry of control systems, dynamical and stochastics systems
Grantee:Marco Antônio Teixeira
Support type: Research Projects - Thematic Grants