Geodesic
Topological and ergodic aspects of partially hyperbolic diffeomorphisms and nonhyperbolic step skew products
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Order and chaos in dynamical systems, Tome 297 (2017), pp. 113-132.

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We review some ergodic and topological aspects of robustly transitive partially hyperbolic diffeomorphisms with one-dimensional center direction. We also discuss step skew-product maps whose fiber maps are defined on the circle which model such dynamics. These dynamics are genuinely nonhyperbolic and exhibit simultaneously ergodic measures with positive, negative, and zero exponents as well as intermingled horseshoes having different types of hyperbolicity. We discuss some recent advances concerning the topology of the space of invariant measures and properties of the spectrum of Lyapunov exponents. 
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L. J. Díaz; K. Gelfert; M. Rams. Topological and ergodic aspects of partially hyperbolic diffeomorphisms and nonhyperbolic step skew products. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Order and chaos in dynamical systems, Tome 297 (2017), pp. 113-132. http://geodesic.mathdoc.fr/item/TM_2017_297_a5/

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