## Journal of Mathematics of Kyoto University

### Exponential decay of correlations for surface semiflows with an expanding direction

Ippei Obayashi

#### Abstract

Dolgopyat [4] showed that a class of Axiom A flows has exponential decay of correlations for smooth observables, and Baladi-Vallée [2] gave a nice interpretation of it on suspension semiflows of one-dimensional expanding countable Markov maps. Avila-Gouëzel-Yoccoz [1] extends the result of Baladi-Vallée to higher dimensional systems.

In this paper we show that a class of non-Markov semiflows also has exponential decay of correlations.

We prove that such exponential decay can be shown on an open dense condition for the suspensions of piecewise expanding maps.

#### Article information

Source
J. Math. Kyoto Univ., Volume 49, Number 2 (2009), 427-440.

Dates
First available in Project Euclid: 22 October 2009

https://projecteuclid.org/euclid.kjm/1256219166

Digital Object Identifier
doi:10.1215/kjm/1256219166

Mathematical Reviews number (MathSciNet)
MR2571851

Zentralblatt MATH identifier
1184.37008

#### Citation

Obayashi, Ippei. Exponential decay of correlations for surface semiflows with an expanding direction. J. Math. Kyoto Univ. 49 (2009), no. 2, 427--440. doi:10.1215/kjm/1256219166. https://projecteuclid.org/euclid.kjm/1256219166