Geodesic
Invariant densities for C¹ maps
Studia Mathematica, Tome 120 (1996) no. 1, pp. 83-88 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm-120-1-83-88
Keywords: cocycle, expanding map, invariant density, absolutely continuous invariant measure 
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Anthony N. Quas. Invariant densities for C¹ maps. Studia Mathematica, Tome 120 (1996) no. 1, pp. 83-88. doi: 10.4064/sm-120-1-83-88

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