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Markov extensions for multi-dimensional dynamical systems. (English) Zbl 0988.37012
The author proves that an arbitrary piecewise invertible dynamical system is isomorphic “in the sense of entropy” with a countable topological Markov chain as soon as one can find some invertibility partition such that
a) the topological entropy of the boundary of the partition is smaller than the total topological entropy;
b) the partition separates orbits outside some set which is neglibible “in the sense of entropy”.
The author also presents a finiteness result and a nontrivial application to a class of multidimensional dynamical systems. Finally he shows that fibered perturbations of products of chaotic smooth interval maps have a finite number of invariant and ergodic probability measures with maximal entropy.

MSC:
37A99 Ergodic theory
37B40 Topological entropy
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