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Article Dans Une Revue Annali della Scuola Normale Superiore di Pisa Année : 2020

ARNOUX-RAUZY INTERVAL EXCHANGE TRANSFORMATIONS

Résumé

The Arnoux-Rauzy systems are defined in [5], both as symbolic systems on three letters and exchanges of six intervals on the circle. In connection with a conjecture of S.P. Novikov, we investigate the dynamical properties of the interval exchanges, and precise their relation with the symbolic systems, which was known only to be a semi-conjugacy; in order to do this, we define a new system which is an exchange of nine intervals (it was described in [3] for a particular case). Our main result is that the semi-conjugacy determines a measure-theoretic isomorphism under an explicit (sufficient) condition, which is satisfied by almost all Arnoux-Rauzy systems for a suitable measure; but, under another condition, the interval exchanges are not uniquely ergodic and the isomorphism does not hold for all invariant measures; finally, we give conditions for these interval exchanges to be weakly mixing.
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Dates et versions

hal-02120138 , version 1 (05-05-2019)

Identifiants

  • HAL Id : hal-02120138 , version 1

Citer

Pierre Arnoux, Julien Cassaigne, Sébastien Ferenczi, Pascal Hubert. ARNOUX-RAUZY INTERVAL EXCHANGE TRANSFORMATIONS. Annali della Scuola Normale Superiore di Pisa, In press. ⟨hal-02120138⟩
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