Symplectic Biliards

Open Access
Author:
Friend, Raymond J
Area of Honors:
Mathematics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Sergei Tabachnikov, Thesis Supervisor
  • Richard Robinett, Honors Advisor
Keywords:
  • symplectic
  • billiards
  • polygonal
  • periodicity
  • dynamical system
  • dynamics
  • dynamical systems
Abstract:
This document introduces a new planar billiards, first coined symplectic billiards in [1]. Symplectic billiards, when applied to polygonal boundaries, offers complicated behaviors with respect to periodicity. Various polygons are considered here, with progress made specifically in describing the behaviors in the affine space of quadrilaterals.