"A generic C<sup>1</sup> expanding map has a singular S-R-B measure" by James T. Campbell and Anthony N. Quas
 

A generic C1 expanding map has a singular S-R-B measure

Abstract

We show that for a generic C1 expanding map T of the unit circle, there is a unique equilibrium state for - log T′ that is an S-R-B measure for T, and whose statistical basin of attraction has Lebesgue measure 1. We also present some results related to the question of whether a generic C1 expanding map preserves a σ-finite measure, absolutely continuous with respect to Lebesgue measure.

Publication Title

Communications in Mathematical Physics

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