Wednesday, June 16, 2010

Periodic points for the beta-transformation in the Pisot and Salem case

Bruno Maia
(Universidade Autónoma de Lisboa)

Abstract: Consider the set of eventually periodic points for the beta-transformation of the unit interval, when beta is a Pisot or a Salem number (these are certain types of algebraic integers). This problem was addressed by Schmidt in 1980, and it was solved for the Pisot (hyperbolic) case. We propose an alternative and equivalent dynamical system to study this set of eventually periodic points. This new system is related to the companion matrix of the minimal polynomial of beta, and there are some connections with the associated toral automorphism.

Wednesday, June 16, 2010
Time: 14h30
Room: B1-01, Complexo Interdisciplinar, UL