On 2-antiparallel encounters on factors of the hyperbolic plane

TL;DR

This paper studies geodesic flows on hyperbolic plane factors, proving the existence of partner orbits for certain encounters, and applies this to validate predictions in quantum chaos.

Contribution

It introduces a method to construct partner orbits for 2-antiparallel encounters and estimates their action differences, extending understanding of orbit correlations.

Findings

Existence of partner orbits for 2-antiparallel encounters

Constructed explicit partner orbits with action estimates

Validated Sieber/Richter's prediction accuracy

Abstract

In this paper, we consider the geodesic flow on factors of the hyperbolic plane. We prove that a periodic orbit including a 2-antiparallel encounter has a partner orbit. We construct the partner orbit and give an estimate for the action different between the orbit pair. Then we apply the result to reprove the accuracy of Sieber/Richter's prediction in [Sieber and Richter, 2001].