Nonuniformly hyperbolic systems arising from coupling of chaotic and gradient-like systems (Q2196696)

The authors study the dynamical behavior of the coupling of two maps, where one is an Anosov diffeomorphism and the other is of gradient type, specifically a N-pole-to-S-pole map of the circle. Two types of coupling are considered in detail: (i) weak coupling, that is, a small perturbation of the uncoupled system; (ii) regular coupling, in which the Anosov map acts on the gradient circle map in a regular way by rotations that can be quite large. The existence of the invariant manifolds is proved and the Sinai-Ruelle-Bowen measures are constructed.