Title: On the relationship between entropy and periodic orbits
Speaker: Bryce Weaver (Xavier University)
Abstract: Via Pesin theory, complexity, measured by entropy, is inexorably linked to structure, namely stable/unstable manifolds. Another such link is the relationship between entropy and growth of periodic orbits. One pioneer result in this area was by G. Margulis in the late ‘60s for geodesics flows on negatively curved manifolds. We explore an adaptation of the technique established by G. Margulis in the case of case of geodesic flows on manifolds with regions of positive curvature. We then close with some settings where there is potential for similar adaptations, in particular the Bunimovich stadium billiards.