On two recurrence problems
Michael Boshernitzan, Eli Glasner
TL;DR
This paper reviews recurrence in topological dynamics, focusing on two open problems related to Poincare-Birkhoff recurrence and moving recurrence, providing partial solutions to the latter.
Contribution
It offers a partial solution to a topological version of the moving recurrence problem, advancing understanding of recurrence phenomena.
Findings
Partial answer to the moving recurrence problem
Clarification of the relation between Poincare and Birkhoff recurrence
Insights into recurrence in topological dynamics
Abstract
We review some aspects of recurrence in topological dynamics and focus on two open problems. The first is an old one concerning the relation between Poincare and Birkhoff recurrence; the second, due to Boshernitzan, is about moving recurrence. We provide a partial answer to a topological version of the moving recurrence problem.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Graph theory and applications · Mathematical Dynamics and Fractals