2018/11/09 by Víctor Ayala, Ayala, Victor, Adriano Da Silva +3 · 1 citation
Computer Science · Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1811.04034
openalex publication_date 2018/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a compact metric space (X; \varrho) and a continuous function f:X→ X, we study the dynamics of the induced map f on the hyperspace of the compact subsets of X. We show how the chain recurrent set of f and its components are related with the one of the induced map. The main result of the paper proves that, under mild conditions, the numbers of chain components of f is greater than the ones of f. Showing the richness in the dynamics of f which cannot be perceived by f.