| Abstract: |
| We introduce a weaker form of the specification property, called ``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) (-$\beta$)-transformations for Yrrap $\beta>1$. 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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