Abstract: We construct Markov partitions for non-invertible and/or singular nonuniformy hyperbolic systems defined on higher dimensional Riemannian manifolds. The generality of the setup covers classical examples not treated so far, such as geodesic flows in closed manifolds, multidimensional billiard maps, and Viana maps, as well as includes all the recent results of the literature. We also provide a wealthy of
applications. Joint work with Ermerson Araujo and Mauricio Poletti.


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