J. Kwiatkowski & Y. Lacroix


Titre: "Morse extensions of rank 1 systems"


Résumé: We investigate Morse finite group extensions of rank 1 sytems. First we make some elementary observations concerning spectral properties of such systems, in connection to harmonic analysis. Then we obtain a necessary and sufficient condition for such an extension to be ergodic, or weakly-mixing, or mixing. We obtain for two ergodic such an equivalent formulation for measure theoretic isomorphism. This is applied to investigating (canonical) factors of such systems in connection with (normal) natural factors.

Also these criterions are used to proving that no countable set of complete invariants is available for the class of these extensions that are mixing.

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