Universität zu Köln

Gutkin, Boris and Osipov, Vladimir (2013). Clustering of Periodic Orbits and Ensembles of Truncated Unitary Matrices. J. Stat. Phys., 153 (6). S. 1049 - 1065. NEW YORK: SPRINGER. ISSN 1572-9613

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Abstract

In present article we consider a combinatorial problem of counting and classification of periodic orbits in dynamical systems on an example of the baker's map. Periodic orbits of a chaotic system can be organized into a set of clusters, where orbits from a given cluster traverse approximately the same points of the phase space but in a different time-order. We show that counting of cluster sizes in the baker's map can be turned into a spectral problem for matrices from truncated unitary ensemble (TrUE). We formulate a conjecture of universality of the spectral edge in the eigenvalues distribution of TrUE and utilize it to derive asymptotics of the second moment of cluster distribution in the regime when both the orbit lengths and the parameter controlling closeness of the orbit actions tend to infinity. The result obtained allows to estimate the size of average cluster for various numbers of encounters in periodic orbit.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Gutkin, Boris UNSPECIFIED UNSPECIFIED UNSPECIFIED Osipov, Vladimir UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-471126
DOI:	10.1007/s10955-013-0859-9
Journal or Publication Title:	J. Stat. Phys.
Volume:	153
Number:	6
Page Range:	S. 1049 - 1065
Date:	2013
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	1572-9613
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language SPECTRA Multiple languages Physics, Mathematical Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/47112