2013/05/08 by Todd Fisher, Fisher, Todd, Rafaël Potrie +3 · 1 citation
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1305.1915
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.