Kyushu Journal of Mathematics
Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116
ON THE ONE-WAY SPECIFICATION PROPERTY AND LARGE DEVIATIONS FOR SYSTEMS WITH NON-DENSE ERGODIC MEASURES
Kenichiro YAMAMOTO
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2018 Volume 72 Issue 1 Pages 71-94

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Abstract

We introduce a weaker form of the specification property, called the ‘one-way specification property', which holds for a broad class of systems whose ergodic measures are not dense in the set of invariant measures, including Smale's horseshoe map, DA map, and (symbolic spaces of) (–β)-transformations for Yrrap β > 1. As an application, we show that these three examples satisfy a level-2 large deviation principle with the normalized Lebesgue measure.

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© 2018 Faculty of Mathematics, Kyushu University
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