IPr* recurrence and nilsystems
V. Bergelson, A. Leibman
TL;DR
This paper proves that nilsystems have the IPr*-recurrence property and that this property characterizes nilsystems, providing a new understanding of their recurrence behavior.
Contribution
It establishes the IPr*-recurrence property as a defining feature of nilsystems, linking recurrence properties to their structural characterization.
Findings
Nilsystems possess the IPr*-recurrence property
The IPr*-recurrence property characterizes nilsystems
Provides a new perspective on recurrence in dynamical systems
Abstract
We prove that nilsystems possess the IPr*-recurrence property and, moreover, are characterized by this property.
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Taxonomy
Topicssemigroups and automata theory · Mathematical Dynamics and Fractals · Computability, Logic, AI Algorithms