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Thermodynamic and multifractal formalism and the Bowen-series map

Technical Report:

Abstract

In the theory of quantum chaos one studies the semiclassical behaviour of quantum mechanical systems whose corresponding classical counterparts exhibit chaos. These systems are sometimes considered as model systems in the theory of quantum chaos since they are well understood from a mathematical point of view. In this work we study the multifractal formalism for the geodesic flow on surfaces with constant negative curvature. The multifractal analysis of measures has been developed in order to characterize the scaling behaviour of measures on attractors of classical chaotic dynamical systems globally. In order to relate the multifractal formalism with quantities usually considered in the study of the geodesic flow on Riemann surfaces with constant negative curvature, it is necessary to establish the assertions of the multifractal formalism in a mathematically rigorous way. This is achieved with the help of the thermodynamic formalism for hyperbolic dynamical systems developed by Ruelle, Bowen and others. (orig.)
Authors:
Rudolph, O [1] 
  1. Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
Publication Date:
Jul 01, 1994
Product Type:
Technical Report
Report Number:
DESY-94-122
Reference Number:
SCA: 661100; PA: DEN-94:0FM602; EDB-95:017556; SN: 95001305321
Resource Relation:
Other Information: PBD: Jul 1994
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; QUANTUM MECHANICS; STOCHASTIC PROCESSES; CLASSICAL MECHANICS; GEODESICS; RIEMANN SPACE; SCALING LAWS; SEMICLASSICAL APPROXIMATION; THERMODYNAMICS; FRACTALS; MEASURE THEORY; ANOMALOUS DIMENSION; HAUSDORFF SPACE; METRICS; ENTROPY; TOPOLOGY; THERMAL EQUILIBRIUM; TOPOLOGICAL MAPPING; SERIES EXPANSION; BOUNDARY CONDITIONS; SCHROEDINGER EQUATION; TRANSFER MATRIX METHOD; ERGODIC HYPOTHESIS; 661100; CLASSICAL AND QUANTUM MECHANICS
OSTI ID:
10105637
Research Organizations:
Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
Country of Origin:
Germany
Language:
English
Other Identifying Numbers:
Journal ID: ISSN 0418-9833; Other: ON: DE95725986; TRN: DE94FM602
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
DEN
Size:
110 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Rudolph, O. Thermodynamic and multifractal formalism and the Bowen-series map. Germany: N. p., 1994. Web.
Rudolph, O. Thermodynamic and multifractal formalism and the Bowen-series map. Germany.
Rudolph, O. 1994. "Thermodynamic and multifractal formalism and the Bowen-series map." Germany.
@misc{etde_10105637,
title = {Thermodynamic and multifractal formalism and the Bowen-series map}
author = {Rudolph, O}
abstractNote = {In the theory of quantum chaos one studies the semiclassical behaviour of quantum mechanical systems whose corresponding classical counterparts exhibit chaos. These systems are sometimes considered as model systems in the theory of quantum chaos since they are well understood from a mathematical point of view. In this work we study the multifractal formalism for the geodesic flow on surfaces with constant negative curvature. The multifractal analysis of measures has been developed in order to characterize the scaling behaviour of measures on attractors of classical chaotic dynamical systems globally. In order to relate the multifractal formalism with quantities usually considered in the study of the geodesic flow on Riemann surfaces with constant negative curvature, it is necessary to establish the assertions of the multifractal formalism in a mathematically rigorous way. This is achieved with the help of the thermodynamic formalism for hyperbolic dynamical systems developed by Ruelle, Bowen and others. (orig.)}
place = {Germany}
year = {1994}
month = {Jul}
}