%ARudolph, O [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik]
%D1994
%I; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
%J
%K71 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
%PMedium: X; Size: 110 p.
%TThermodynamic and multifractal formalism and the Bowen-series map
%XIn 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.)
%0Technical Report
Germany Journal ID: ISSN 0418-9833; Other: ON: DE95725986; TRN: DE94FM602 DEN English