Most expanding maps have no absolutely continuous invariant measure
Quas, Anthony
Studia Mathematica, Tome 133 (1999), p. 69-78 / Harvested from The Polish Digital Mathematics Library
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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 C1 expanding map of the circle has no absolutely continuous invariant probability measure. This is in contrast with the situation for C2 or C1+ε expanding maps, for which it is known that there is always a unique absolutely continuous invariant probability measure.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:216623 
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     pages = {69-78},
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Quas, Anthony. Most expanding maps have no absolutely continuous invariant measure. Studia Mathematica, Tome 133 (1999) pp. 69-78. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv134i1p69bwm/

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