Stochastic stability for partially hyperbolic diffeomorphisms with mostly expanding and contracting centers

TL;DR

This paper establishes the stochastic stability of a class of partially hyperbolic diffeomorphisms with specific expanding and contracting center behaviors, contributing to the understanding of their robustness under random perturbations.

Contribution

It proves stochastic stability for a broad class of partially hyperbolic diffeomorphisms with two centers exhibiting distinct Lyapunov exponent signs.

Findings

Proves stochastic stability for the class of systems studied.

Identifies conditions on Gibbs u-states related to Lyapunov exponents.

Extends understanding of stability in partially hyperbolic dynamics.

Abstract

We prove the stochastic stability of an open class of partially hyperbolic diffeomorphisms, each of which admits two centers $E^c_1$ and $E^c_2$ such that any Gibbs $u$-state admits only positive (resp. negative) Lyapunov exponents along $E^c_1$ (resp. $E^c_2$).