EVENT DETAILS AND ABSTRACT

Title: On a two-parameter family of continued fraction transformations
Speaker: Ilie Ugarcovici
Speaker Info: DePaul
Brief Description:
Special Note:
Abstract:

I will describe a class of one-dimensional maps and related continued fraction algorithms suggested for consideration by Don Zagier. We prove that the associated two-dimensional realizations of the natural extension maps have domains with finite rectangular structure for all parameter pairs with the exception of a one-dimensional null measure set that we completely describe. We also show how these geometric properties help us study the invariant measures and other ergodic properties of the associated Gauss-like maps. This is joint work with S. Katok.