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Most expanding maps have no absolutely continuous invariant measure

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Quas A. N.

Studia Mathematica

1999

tom 134

nr 1

69-78

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.

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1 Studia Mathematica

1 Quas A. N.

1 1999

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Most expanding maps have no absolutely continuous invariant measure