Work

Quantitative recurrence for $T,T^{-1}$ tranformation

Year: 2023

Type: preprint

Abstract: We are interested in the study of the asymptotic behaviour of return times in small balls for the $T,T^{-1}$-transformation. We exhibit different asymptotic behaviours (different scaling, different limit point process) depending on the respective dimensions of the measures of the two underlying dynamical systems. It behaves either as for the direct product of the underlying systems, or as for the Z-extension of the driving system (also studied in this article), or as a more sophisticated process.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2310.17969

Authors: Pène, Françoise, Saussol, Benoit

Institutions: Université de Bretagne Occidentale, Université de Bretagne Sud, Laboratoire de Mathématiques de Bretagne Atlantique, Institut de Mécanique et d'Ingénierie de Bordeaux, Institut de Mathématiques de Marseille

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Awards: Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation, Geometry and Asymptotics of large surfaces

OpenAlex ID: W4387963151

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