martedi' 18-10-2005 (14:00) - Sala Conferenze del Centro di Ricerca Matematica Ennio De Giorgi Rie NATSUI (Nihon University, Tokyo) : On the isomorphism problem for a 1-parameter family of $\alpha$-Farey maps

SEMINARIO DI SISTEMI DINAMICI (olomorfi e dintorni) Abstract : We consider the isomorphism problem for a $1$-parameter family of interval maps, called $\alpha$-Farey maps for $\frac{1}{2} \le \alpha \le 1$, as a class of non-invertible infinite measure preserving transformations. These maps are associated with the mediant convergents induced from the $\alpha$-continued fractions. The main result is that $\alpha$-Farey maps are not isomorphic to each other for $\frac{1}{2} \le \alpha \le 1$, on the other hand, their natural extensions are isomorphic. To prove this result, we construct their natural extensions as two dimensional maps.

Giulia Curciarello Segreteria Didattica tel: 050-2213219 e-mail curciare@dm.unipi.it

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