Event Detail

Event Type: 
Number Theory Seminar
Date/Time: 
Tuesday, April 5, 2022 - 10:00 to 10:50
Location: 
Zoom only, contact Clayton Petsche for Zoom information

Speaker Info

Local Speaker: 
Abstract: 

It remains a mystery how Gauss calculated the key tool to compute probabilities of events expressed in terms of regular continued fractions: the invariant measure of the
underlying interval map. Nakada and co-authors (1977) showed how this invariant measure can be easily rediscovered by the use of a planar extension of the interval map. In the 1980s this use of planar extensions was exploited to begin the study of various families of interval maps. In this century, great progress has been made, with emphasis on the “measure theoretic entropy” of the maps. We briefly explain the basic terms and mechanisms, and present results giving alternate approaches to determining key dynamical properties of planar extensions of continued fraction-like maps. Based upon joint work with Calta and Kraaikamp, and with Arnoux.