Invariant densities for C¹ maps
Volume 120 / 1996
Studia Mathematica 120 (1996), 83-88
DOI: 10.4064/sm-120-1-83-88
Abstract
We consider the set of $C^1$ expanding maps of the circle which have a unique absolutely continuous invariant probability measure whose density is unbounded, and show that this set is dense in the space of $C^1$ expanding maps with the $C^1$ topology. This is in contrast with results for $C^2$ or $C^{1+ε}$ maps, where the invariant densities can be shown to be continuous.
