Contracting on average iterated function systems by metric change

2021/12/13 by Katrin Gelfert, Graccyela Salcedo, Gelfert, Katrin +1 · 1 citation
Mathematics · #37B05 #37E10 37E10 37E10 #37H99 #37Hxx #60G50 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2112.06819

openalex publication_date 2021/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We study contraction conditions for an iterated function system of continuous maps on a metric space which are chosen randomly, identically and independently. We investigate metric changes, preserving the topological structure of the space, which turn the IFS into one which is contracting on average. For the particular case of a system of C¹-diffeomorphisms of the circle which is proximal and does not have a probability measure simultaneously invariant by every map, we derive a strongly equivalent metric which contracts on average.

Cited by

• Concentration inequalities for random dynamical systems

Related

• On the fine structure of stationary measures in systems which contract-on-average
• Random iterated function systems with smooth invariant densities
• Empirical processes of iterated maps that contract on average
• Contraction in the Wasserstein metric for some Markov chains, and\n applications to the dynamics of expanding maps
• Path--Averaged Contractions: A New Generalization of the Banach Contraction Principle