ISBN 9783843915755

978-3-8439-1575-5, Reihe Mathematik

Hien Minh Huynh
Partner Orbits and Action Differences on Compact Factors of the Hyperbolic Plane

150 Seiten, Dissertation Universität Köln (2014), Softcover, B5

Zusammenfassung / Abstract

Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for quantum systems. However, a mathematically rigorous treatment is still missing. To establish a detailed understanding, we consider the geodesic flow on compact factors of the hyperbolic plane. We prove the existence of the periodic partner orbit for a given periodic orbit which has a small-angle self-crossing in configuration space, and we derive an estimate for the action difference of the partners. We also provide an inductive argument to deal with higher-order encounters.