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Dynamics, Geometry and Groups Seminar

Friday, September 23rd, 2022

Time: 10:00 a.m.  Place: Jeffery Hall, Room 422

Speaker: Henry Kavle (¾ÅÐãÖ±²¥)

Title: A Morse index-Maslov index correspondence for convex billiards

Abstract: In 1976, J.J. Duistermaat proved a general correspondence between the Morse index of a trajectory arising as a critical point of a variational problem and the Maslov index of a path of symplectic matrices describing the linearized flow along the trajectory in phase space. We will sketch an analogous correspondence for discrete time dynamics, emphasizing concrete computations for periodic orbits in smooth convex billiard tables. Time permitting, we will show that these indices allow us to determine the linear stability of periodic trajectories.