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

Autor(es)

Rodrigues, Christian S. ^[1] ; Ruffino, Paulo R. C. ^[2]

Afiliação do(s) autor(es)

^[1] Max Planck Inst Math Sci, D-04103 Leipzig - Germany

^[2] Univ Estadual Campinas, Dept Matemat, BR-13 08385 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Stochastics and Dynamics; v. 15, n. 3 SEP 2015.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 11/50151-0 - Fenômenos dinâmicos em redes complexas: fundamentos e aplicações
• Beneficiário: Elbert Einstein Nehrer Macau
• Linha de fomento: Auxílio à Pesquisa - Temático
• Processo FAPESP: 12/18780-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Marco Antônio Teixeira
• Linha de fomento: Auxílio à Pesquisa - Temático