# American Institute of Mathematical Sciences

July  2017, 37(7): 3867-3903. doi: 10.3934/dcds.2017163

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

 1 Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5,40126 Bologna, Italy 2 Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Via Irnerio 46,40126 Bologna, Italy

Received  January 2015 Revised  February 2017 Published  April 2017

Fund Project: The author was partially supported by PRIN Grant 2012AZS52J 001 (MIUR, Italy).

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.

Citation: Marco Lenci. Uniformly expanding Markov maps of the real line: Exactness and infinite mixing. Discrete & Continuous Dynamical Systems - A, 2017, 37 (7) : 3867-3903. doi: 10.3934/dcds.2017163
##### References:

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##### References:
A uniformly expanding Markov map ${\mathbb{R}} \to {\mathbb{R}}$.
An example of a quasi-lift of an expanding circle map.
A finite modification of a quasi-lift of a circle map, constructed with the procedure given in Section 3.2, for the case $\mu_o = m$.
A map $T$ associated a random walk. The marks on the abscissa indicate the Markov intervals $I_{jk}$, while those on the ordinate represent the intervals $[k, k+1]$.
A rough sketch of the map $T$ of Counterexample 2. The bold segments on the abscissa indicate the set $X$. The bold parts of the graph of $T$ represent $T|_X$, which is invertible.
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