Universität zu Köln

Hien, HM (2016). Partner orbits and action differences on compact factors of the hyperbolic plane. II: Higher-order encounters. Physica D, 314. S. 35 - 54. AMSTERDAM: ELSEVIER. ISSN 1872-8022

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Abstract

Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at the classical side of the problem and determine orbit pairs consisting of orbits which have similar actions. We specialize to the geodesic flow on compact factors of the hyperbolic plane as a classical chaotic system. The companion paper (Huynh and Kunze, 2015) proved the existence of a unique periodic partner orbit for a given periodic orbit with a small-angle self-crossing in configuration space that is a 2-encounter and derived an estimate for the action difference of the orbit pair. In this paper, we provide an inductive argument to deal with higher-order encounters: we prove that a given periodic orbit including an L-parallel encounter has (L - 1)! - 1 partner orbits; we construct partner orbits and give estimates for the action differences between orbit pairs. (C) 2015 Elsevier B.V. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Hien, HM UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-293553
DOI:	10.1016/j.physd.2015.10.001
Journal or Publication Title:	Physica D
Volume:	314
Page Range:	S. 35 - 54
Date:	2016
Publisher:	ELSEVIER
Place of Publication:	AMSTERDAM
ISSN:	1872-8022
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language PERIODIC-ORBITS Multiple languages Mathematics, Applied; Physics, Fluids & Plasmas; Physics, Multidisciplinary; Physics, Mathematical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/29355