Growth Rate of Periodic orbits for Geodesic Flows on Surfaces with Regions of Positive Curvature
Open Access
Author:
Weaver, Bryce A.
Graduate Program:
Mathematics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
May 07, 2008
Committee Members:
Anatole Katok, Committee Chair/Co-Chair Yakov B Pesin, Committee Member Omri Sarig, Committee Member David Gerard Abler, Committee Member
Keywords:
non-uniformly hyperbolic growth of periodic orbits dynamical systems geodesic flows positive curvature Margulis measure
Abstract:
We construct a Margulis measure on the unit tangent bundle of compact surfaces that have regions of positive curvature. This measure is then used to obtain a lower bound C$grave{e}$saro estimate on $ds P_epsilon(t)$, which is the number of periodic orbits of period $t pm epsilon$ for the geodesic flow. This is the first step toward obtaining precise asymptotics and suggests that $ds P_epsilon(t)$ grows like $ds frac{e^{kt}}{t}$, for some constant $k$.
