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Dynamical coherence of partially hyperbolic diffeomorphisms of tori isotopic to Anosov

Research paper by Todd Fisher, Rafael Potrie, Martín Sambarino

Indexed on: 13 Apr '14Published on: 13 Apr '14Published in: Mathematische Zeitschrift



Abstract

We show that partially hyperbolic diffeomorphisms of \(d\)-dimensional tori isotopic to an Anosov diffeomorphism, where the isotopy is contained in the set of partially hyperbolic diffeomorphisms, are dynamically coherent. Moreover, we show a global stability result, i.e. every partially hyperbolic diffeomorphism as above is leaf-conjugate to the linear one. As a consequence, we obtain intrinsic ergodicity and measure equivalence for partially hyperbolic diffeomorphisms with one-dimensional center direction that are isotopic to Anosov diffeomorphisms through such a path.