Generic expanding maps without absolutely continuous invariant $\sigma$-finite measure

arxiv: math/0608062 · v1 · submitted 2006-08-02 · 🧮 math.DS

Generic expanding maps without absolutely continuous invariant σ-finite measure

Artur Avila , Jairo Bochi This is my paper

classification 🧮 math.DS

keywords absolutelycontinuousexpandingfinitegenericinvariantmeasuresigma

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We show that a $C^1$-generic expanding map of the circle has no absolutely continuous invariant $\sigma$-finite measure.

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