Gibbs–Markov structures and limit laws for partially hyperbolic attractors with mostly expanding central direction

Gibbs-markov Structures and Limit Laws for Partially Hyperbolic Attractors with Mostly Expanding Central Direction

— We consider a partially hyperbolic set K on a Riemannian manifold M whose tangent space splits as TKM = E cu⊕Es, for which the centre-unstable direction E expands non-uniformly on some local unstable disk. We show that under these assumptions f induces a Gibbs-Markov structure. Moreover, the decay of the return time function can be controlled in terms of the time typical points need to achiev...

GIBBS-MARKOV STRUCTURES AND LIMIT LAWS FOR PARTIALLY HYPERBOLIC ATTRACTORS WITH MOSTLY EXPANDING CENTRAL DIRECTION by

— We consider a partially hyperbolic set K on a Riemannian manifold M whose tangent space splits as TKM = Ecu⊕Es, for which the centre-unstable direction E expands non-uniformly on some local unstable disk. We show that under these assumptions f induces a Gibbs-Markov hyperbolic structure. Moreover, the decay of the return time function can be controlled in terms of the time typical points need...

SRB measures for partially hyperbolic systems whose central direction is mostly expanding

SRB measures for partially hyperbolic systems whose central direction is mostly expanding

Stable Ergodicity for Partially Hyperbolic Attractors with Negative Central Exponents

We establish stable ergodicity of diffeomorphisms with partially hyperbolic attractors whose Lyapunov exponents along the central direction are all negative with respect to invariant SRBmeasures.