Uniformly expanding Markov maps of the real line: exactness and infinite mixing

Abstract

We give a fairly complete characterization of the exact components of a large class of uniformly expanding Markov maps of $\mathbb{R}$. Using this result, for a class of $\mathbb{Z}$-invariant maps and finite modifications thereof, we prove certain properties of infinite mixing recently introduced by the author.

Final version to be published in Discrete and Continuous Dynamical Systems A. 47 pages, 5 figures. Labeling of appendices (and related wording) may differ from published version

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Cited by in corpus (4)

• Infinite mixing for one-dimensional maps with an indifferent fixed point
• Pointwise convergence of Birkhoff averages for global observables
• Global-local mixing for the Boole map
• Extensions of exact and K-mixing dynamical systems