Journal of Mathematics of Kyoto University

Exponential decay of correlations for surface semiflows with an expanding direction

Ippei Obayashi

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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

Permanent link to this document
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


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