AVVISO DI SEMINARIO

Sistemi Dinamici

Martedì 18 ottobre 2005 ore 14.00

Centro di Ricerca Matematica Ennio De Giorgi

(Sala Conferenze Collegio Puteano)

Rie NATSUI

Nihon University, Tokyo

Terrà un seminario dal titolo:

"On the isomorphism problem for a 1-parameter family of $\alpha$-Farey maps"

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.

Tutti gli interessati sono invitati a partecipare.

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