Work

A pointwise ergodic theorem along return times of rapidly mixing systems

Year: 2025

Type: article

Abstract: We introduce a new class of sparse sequences that are ergodic and pointwise universally ‐good for ergodic averages; that is, sequences along which the ergodic averages converge almost surely to the projection to invariant functions. These sequences are generated randomly as return or hitting times in systems exhibiting a rapid correlation decay. This can be seen as a natural variant of Bourgain's return times theorem. For example, we obtain that for any , the sequence is ergodic and pointwise universally ‐good for Lebesgue almost every . Our approach builds on techniques developed by Frantzikinakis, Lesigne and Wierdl in their study of sequences generated by independent random variables, which we adapt to the non‐independent case.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70184

Authors: Sebastián Donoso, Alejandro Maass, Vicente Saavedra‐Araya

Institutions: Centre National de la Recherche Scientifique, Center for Mathematical Modeling, University of Chile, Millenium Institute Center for Genome Regulation, University of Warwick

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: Institut Català de Nanociència i Nanotecnologia, Agencia Nacional de Investigación y Desarrollo