Convergence uniforme des moyennes ergodiques des fonctions continues

2010/04/15 by Jean-François Bertazzon, Bertazzon, Jean-François
Mathematics · #37A05 #37B05 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37A05 #msc:37B05

paper · pdf · doi:10.48550/arxiv.1004.2568

This paper has been withdrawn by the author. 29 pages, article in the course of rewriting

arxiv created 2010/07/13 · arxiv updated 2013/03/18

Abstract

The goal of this work is to study the space of continuous functions whose ergodic averages converge everywhere towards a continuous function. We will connect, as in the case of a metric study, the convergence of the ergodic averages and the projection of continuous functions on the subspace of invariant functions. We will see that this determines the continuity of the projection of the system onto a certain factor.

Related

• Uniform convergence on subspaces in von Neumann's ergodic theorem with continuous time
• Absolute and Unconditional Convergence of Series of Ergodic Averages and Lebesgue Derivatives
• Pointwise Convergence of Ergodic Averages in Orlicz Spaces
• Convergence of multiple ergodic averages
• Slow convergence almost everywhere of ergodic averages