Geometry MMA Seminar: Birkhoff Averages and the Breakdown of Invariant Sets

Speaker: Evelyn Sander, George Mason University

Title:   Birkhoff Averages and the Breakdown of Invariant Sets

Abstract:  The dynamics of an integrable Hamiltonian or volume-preserving systems consists of quasiperiodic motion on invariant tori. As such a system is perturbed, KAM theory guarantees that some of these tori persist, whereas others are replaced by periodic orbits, islands, and chaotic regions. The tori that persist the longest as the perturbation increases are referred to as the most robust tori, and it is of great interest to understand how to characterize the frequency vectors of these tori.

I will discuss numerical investigations in collaboration with James Meiss.  These methods make it possible to distinguish between chaotic regions, islands, and invariant tori, as well as to calculate the frequency vectors of these tori.

This talk is designed to be accessible to non-experts without any expectation of prior knowledge of the topic presented. 

Time: Monday, March 28, 2022 - 10:30am-11:45am

Place: Exploratory Hall, Room 4106 - Mask will be required for in-person attendance.

In person and on Zoom