ON THE ONE-WAY SPECIFICATION PROPERTY AND LARGE DEVIATIONS FOR SYSTEMS WITH NON-DENSE ERGODIC MEASURES

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.