2014/12/02 by Benoît Kloeckner, Kloeckner, Benoit, Artur O. Lopes +3 · 3 citations
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1412.0848
openalex publication_date 2014/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We employ techniques from optimal transport in order to prove decay of\ntransfer operators associated to iterated functions systems and expanding maps,\ngiving rise to a new proof without requiring a Doeblin-Fortet (or Lasota-Yorke)\ninequality. Our main result is the following. Suppose T is an expanding\ntransformation acting on a compact metric space M and A: M \→ \ℝ a\ngiven fixed H "older function, and denote by L the Ruelle operator\nassociated to A. We show that if L is normalized (i.e. if L(1)=1), then\nthe dual transfer operator L^* is an exponential contraction on the set of\nprobability measures on M with the 1-Wasserstein metric.Our approach is\nflexible and extends to a relatively general setting, which we name Iterated\nContraction Systems. We also derive from our main result several dynamical\nconsequences; for example we show that Gibbs measures depends in a\nLipschitz-continuous way on variations of the potential.\n