Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

Understand

We employ techniques from optimal transport in order to prove decay of transfer operators associated to iterated functions systems and expanding maps, giving rise to a new proof without requiring a Doeblin-Fortet (or Lasota-Yorke) inequality.

• Our main result is the following.
• Suppose $T$ is an expanding transformation acting on a compact metric space $M$ and $A: M \to \mathbb{R}$ a given fixed H{\"o}lder function, and denote by $L$ the Ruelle operator associated to $A$.
• We show that if $L$ is normalized (i.e.