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George Mason University
Events

Geometry MMA Seminar: Dynamics of quaternionic continued fractions

Aug 28, 2023, 10:30 - 11:30 AM

 

Speaker:  Anton Lukyanenko, George Mason University

Title:   Dynamics of quaternionic continued fractions

Abstract:  Regular continued fractions (CF) express a number in [0,1) as a descending fraction with positive integer entries, and appear in a wide range of applications. In particular, the associated Gauss mapping T(x)={1/x} is a classical example of a chaotic dynamical system with well-understood long-term behavior. 

In this talk, I will discuss how one generalizes CFs to higher-dimensional spaces (including the more exotic quaternionic and Heisenberg CFs) and share some recent results on mixing properties and invariant measures. 

The talk will be largely self-contained and feature many illustrations and 3D prints.

 

Time: Monday, August 28 – 10:30am-11:30am

Place: Exploratory Hall, Room 4106