Geodesic
Most expanding maps have no absolutely continuous invariant measure
Studia Mathematica, Tome 134 (1999) no. 1, pp. 69-78 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We consider the topological category of various subsets of the set of expanding maps from a manifold to itself, and show in particular that a generic $C^1$ expanding map of the circle has no absolutely continuous invariant probability measure. This is in contrast with the situation for $C^2$ or $C^{1+ε}$ expanding maps, for which it is known that there is always a unique absolutely continuous invariant probability measure.
DOI : 10.4064/sm-134-1-69-78
Keywords: $C^1$ expanding map, Ruelle-Perron-Frobenius operator 
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Anthony N. Quas. Most expanding maps have no absolutely continuous invariant measure. Studia Mathematica, Tome 134 (1999) no. 1, pp. 69-78. doi: 10.4064/sm-134-1-69-78

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