Density of the set of symbolic dynamics with all ergodic measures supported on periodic orbits

2014/10/21 by Tatiane Cardoso Batista, Batista, T. C., Juliano dos Santos Gonschorowski +3
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1410.5857

openalex publication_date 2014/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be the Cantor set. We prove that arbitrarily close to a homeomorphism T:K→ K there exists a homeomorphism \widetilde T:K→ K such that the α-limit and the ω-limit of every orbit is a periodic orbit. We also prove that arbitrarily close to an endomorphism T:K→ K there exists an endomorphism \widetilde T:K→ K close to T such that every orbit is finally periodic.

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