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60 years of dynamics and number expansions

Matching for alpha-continued fractions

speaker: Wolfgang Steiner (Institut de Recherche en Informatique Fondamentale)

abstract: For a family of alpha-continued fraction maps $T_\alpha$, we say that $\alpha$ is in the matching set if there are positive integers $M, N$ such that $T_z^M(z-1) = T_z^N(z)$ holds for all $z$ in a neighbourhood of $\alpha$. In recent joint work with Carlo Carminati, Niels Langeveld and Hitoshi Nakada, we focus on the map $T_\alpha(x) = 1x - 1/x+1-\alpha$ defined by Tanaka and Ito (1981). For alpha-Rosen continued fractions, some matching intervals were given in joint work with Karma Dajani and Cor Kraaikamp (2009).

timetable:
Wed 12 Dec, 12:15 - 13:00, Aula Dini
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