Generic expanding maps without absolutely continuous invariant σ-finite measure

2006/08/02 by Artur Avila, Jairo Bochi, Avila, Artur +1
Mathematics · #Advanced Topics in Algebra #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · doi:10.48550/arxiv.math/0608062

openalex publication_date 2006/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that a C¹-generic expanding map of the circle has no absolutely continuous invariant σ-finite measure.

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