Work

Random Dynamical Systems on the circle without a finite orbit

Year: 2025

Type: preprint

Abstract: In this paper, we study Random Dynamical Systems (RDSs) of homeomorphisms on the circle without a finite orbit. We characterize the topological dynamics of the associated semigroup by identifying the existence of invariant sets which are finite unions of intervals. We describe the accumulation points of the average orbit of the transfer operator. For each ergodic stationary measure, we demonstrate interesting properties of its weight function on the circle. Relationships between the minimal sets of an RDS and its inverse RDS are also established.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2501.12158

Authors: Malicet, Dominique, Salcedo, Graccyela

Institutions: Centre National de la Recherche Scientifique, Centre de Physique Théorique, Laboratoire d’Analyse et de Mathématiques Appliquées, Institut Polytechnique de Paris, Université Gustave Eiffel

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Fundação de Amparo à Pesquisa do Estado de São Paulo, Uniwersytet Mikolaja Kopernika w Toruniu

Award: G7465036842

OpenAlex ID: W4406745853

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