R440, Astronomy-Mathematics Building, NTU
Speaker(s):
Lien-Yung Kao (George Washington University)
Organizer(s):
Jung-Chao Ban (National Chengchi University)
Chih-Hung Chang (National University of Kaohsiung)
Title:
Entropy, Counting and Equidistribution for Hyperbolic Flows
Abstract:
In this mini-course, we aim to have a discuss the prime orbit theorem. For hyperbolic flows over compact metric spaces, the prime orbit theorem indicates the growth rate of closed orbits can be depicted by the topological entropy of the flow. An immediate application is a result in Margulis’ (1978 Fields Medalist) thesis about counting closed geodesics on negatively curved compact manifolds.
We will discuss two approaches to this problem, namely, Parry-Pollicott’s Zeta function approach and Lalley’s Renewal Theorem approach. The common background of these two approaches is Thermodynamic Formalism for compact symbolic dynamical systems. This mini-course is designed students and will start from scratch. The lectures will mostly follow Parry-Pollicott’s book [PP90] and Lalley’s paper [Lal89].
References:
[Lal89] Steven P. Lalley, Renewal theorems in symbolic dynamics, with applications to geodesic flows, non-Euclidean tessellations and their fractal limits, Acta Math. 163 (1989), no. 1-2, 1–55. MR 1007619
[PP90] William Parry and Mark Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics, Astérisque 187-188 (1990), 1–268.
Registration: (Deadline: 4/13)
https://forms.gle/bt7UqRUnKUXLmJVSA
