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.
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Received: 8 December 2000 / Accepted: 27 March 2001
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Campbell, J., Quas, A. A Generic C1 Expanding Map¶has a Singular S–R–B Measure. Commun. Math. Phys. 221, 335–349 (2001). https://doi.org/10.1007/s002200100491
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DOI: https://doi.org/10.1007/s002200100491