On Equilibrium States for Partially Hyperbolic Horseshoes
arXiv:1505.07742 · doi:10.1017/etds.2016.21
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.
29 pages, 7 figures