Finitely presented dynamical systems

1987/12/01 by David Fried · 3 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Mathematical Dynamics and Fractals #Theoretical and Computational Physics

paper · pdf · doi:10.1017/s014338570000417x

openalex publication_date 1987/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21

Abstract

Abstract We extend results of Bowen and Manning on systems with good symbolic dynamics. In particular we identify the class of dynamical systems that admit Markov partitions. For these systems the Manning-Bowen method of counting periodic points is explained in terms of topological coincidence numbers. We show, in particular, that an expansive system with a finite cover by rectangles has a rational zeta function.

Cited by

• On Sets of Periodic Orbit Lengths in Finitely Presented Dynamical Systems
• Coding and tiling of Julia sets for subhyperbolic rational maps
• Resolving extensions of finitely presented systems

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