Topological and statistical attractors for interval maps

2021/09/09 by Vilton Pinheiro, Pinheiro, Vilton
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2109.04579

openalex publication_date 2021/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use the concept of Baire Ergodicity and Ergodic Formalism introduced to study topological and statistical attractors for interval maps, even with discontinuities. For that we also analyze the \em wandering intervals attractors. As a result, we establish the finiteness of the non-periodic topological attractors for piecewise C² maps with discontinuities. For C² interval maps without discontinuities, we show the coincidence of the statistical attractors with the topological ones and we calculate the upper Birkhoff averages of continuous functions for generic points, even when the map has abundance of historical behavior.

Citations

• Ergodic Formalism for topological Attractors and historic behavior

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