Year: 2006
Type: article
Abstract: The question on the recurrence rate of a dynamical system in a metric space of finite Hausdorff measure is considered. For such systems upper bounds for the rate of simple recurrence are due to Boshernitzan and ones for the rate of multiple recurrence to the present author. The paper is concerned with finding lower bounds for the rate of multiple recurrence. More precisely, an example of a dynamical system (an odometer or a von Neumann transformation) with a low rate of multiple recurrence is constructed. Behrend's theorem on sets containing no arithmetic progressions is used in the proof.
Source: Sbornik Mathematics
Author: I D Shkredov
Institution: Lomonosov Moscow State University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2091972605