Displaying similar documents to “Commuting expanding dynamics.”

Most expanding maps have no absolutely continuous invariant measure

Anthony Quas (1999)

Studia Mathematica

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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.