## Hiroshima Mathematical Journal

### Measures with maximum total exponent and generic properties of $C^{1}$ expanding maps

#### Abstract

We show that a generic $C^{1}$ expanding map on a compact Riemannian manifold has a unique measure of maximum total exponent which is fully supported and of zero entropy. We also show that for $r\ge 2$ a generic $C^{r}$ expanding map does not have fully supported measures of maximum total exponent.

#### Article information

Source
Hiroshima Math. J., Volume 43, Number 3 (2013), 351-370.

Dates
First available in Project Euclid: 7 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1389102580

Digital Object Identifier
doi:10.32917/hmj/1389102580

Mathematical Reviews number (MathSciNet)
MR3161322

Zentralblatt MATH identifier
1347.37056

#### Citation

Morita, Takehiko; Tokunaga, Yusuke. Measures with maximum total exponent and generic properties of $C^{1}$ expanding maps. Hiroshima Math. J. 43 (2013), no. 3, 351--370. doi:10.32917/hmj/1389102580. https://projecteuclid.org/euclid.hmj/1389102580

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