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Deterministic representation for position dependent random maps
Sub-actions for young towers
1. | University of Houston, Houston, TX 77204-3008, United States |
$\phi \leq \theta \circ T - \theta + m(\phi, T)$
where $m(\phi, T)=$sup{$\int \phi d\mu:\mu$ is an invariant probability measure for $ T$}. The existence and regularity of sub-actions are important for the study of optimizing measures. We prove the existence of Hölder sub-actions for Lipschitz functions on certain classes of Manneville-Pomeau type maps. We also construct locally Hölder sub-actions for Lipschitz functions on Young Towers. In some settings (uniform hyperbolicity and Manneville-Pomeau maps) this implies Hölder sub-actions for the underlying system modeled by the Tower.
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