AN ERGODIC SYSTEM IS DOMINANT EXACTLY WHEN IT HAS POSITIVE ENTROPY
un système ergodique est dominant quand il a une entropie positive
Résumé
An ergodic dynamical system X is called dominant if it is isomorphic to a generic extension of itself. It was shown in [8] that Bernoulli systems with finite entropy are dominant. In this work we show first that every ergodic system with positive entropy is dominant, and then that if X has zero entropy then it is not dominant.
Domaines
Mathématiques [math]
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