How much information about a dynamical system do its recurrences contain?

2007/06/27 by Geoffrey R. Robinson, Geoffrey Robinson, Robinson, Geoffrey +2
Mathematics · Physics and Astronomy · #11B37 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:11B37

paper · pdf · doi:10.48550/arxiv.0706.4032

9 pages, 0 figures

openalex publication_date 2007/06/27 · arxiv created 2007/07/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that, under suitable assumptions, Poincare recurrences of a dynamical system determine its topology in phase space. Therefore, dynamical systems with the same recurrences are topologically equivalent.

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