Invariant densities for C¹ maps

Anthony N. Quas

ArticleOriginal scientific text

Title

Invariant densities for C¹ maps

Authors ¹

Affiliations

Statistical Laboratory, Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge CB2 1SB, England

Abstract

We consider the set of

C^{1}

expanding maps of the circle which have a unique absolutely continuous invariant probability measure whose density is unbounded, and show that this set is dense in the space of

C^{1}

expanding maps with the

C^{1}

topology. This is in contrast with results for

C^{2}

or

C^{1 + ε}

maps, where the invariant densities can be shown to be continuous.

Keywords

ENG

cocycle, expanding map, invariant density, absolutely continuous invariant measure

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Title

Invariant densities for C¹ maps

Affiliations

Abstract

Keywords

Bibliography