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arXiv · 1505.07742

On Equilibrium States for Partially Hyperbolic Horseshoes

Isabel Rios·Jaqueline Siqueira
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Abstract

We prove existence and uniqueness of equilibrium states for a family of partially hyperbolic systems, with respect to Holder continuous potentials with small variation. The family comes from the projection, on the center-unstable direction, of a family of partially hyperbolic horseshoes introduced in [Díaz,L., Horita,V., Rios, I., Sambarino, M., Destroying horseshoes via heterodimensional cycles: generating bifurcations inside homoclinic classes, Ergodic Theory and Dynamical Systems, 2009]. For the original three dimensional system, we consider potentials with small variation, constant on local stable manifolds, obtaining existence and uniqueness of equilibrium states.

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Isabel Rios, Jaqueline Siqueira. 2015-05-28. On Equilibrium States for Partially Hyperbolic Horseshoes. https://doi.org/10.1017/etds.2016.21

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