Natural extensions and invariant measures for continued fractions
Expositor: Pierre Arnoux
Instituição: Univ. de Aix-Marseille
Data e Horário: 23/05/18 | 17h:30min
RESUMO: The question of invariant measures for continued fractions goes back two centuries, to a letter of Gauss in 1812. In this lecture, I will show how to build a model of the natural extension for a continued fraction, with invariant Lebesgue measure. In many cases, this allow to give an explicit formula for an invariant density; it may also hint to a suspension flow, which gives a geometric interpretation to the continued fraction. After showing how to build the extension, using a variant of Hutchinson fixed point theorem, I will give several examples and applications, and some open problems.