Smoothness of invariant density for expanding transformations in higher dimensions.
Adl-Zarabi, Kourosh, Proppe, Harald (2000)
Journal of Applied Mathematics and Stochastic Analysis
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Adl-Zarabi, Kourosh, Proppe, Harald (2000)
Journal of Applied Mathematics and Stochastic Analysis
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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 expanding map of the circle has no absolutely continuous invariant probability measure. This is in contrast with the situation for or expanding maps, for which it is known that there is always a unique absolutely continuous invariant probability measure.
Michael Benedicks, Marcelo Viana (2006)
Annales de l'I.H.P. Analyse non linéaire
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Radu Saghin, Zhihong Xia (2009)
Annales de l'I.H.P. Analyse non linéaire
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