交通流经济论文.pdf

Communications in Nonlinear Science and Numerical Simulation 8 (2003) 137–148 /locate/cnsns Weak chaos and anomalous transport: a deterministic approach Roberto Artuso *, Giampaolo Cristadoro Dipartimento di Scienze Chimiche, Fisiche e Matematiche, Istituto Nazionale di Fisica della Materia, Unitaa di Como, Universitaa dellInsubria and Center for the Study of Dynamical Systems, Via Valleggio , I-22100 Como, Italy Abstract We review how transport properties for chaotic dynamical systems may be studied through cycle expan sions, and show how anomalies can be quantitatively described by hierarchical sequences of periodic orbits. 2003 Elsevier B.V. All rights reserved. PACS: 05.45.+b Keywords: Anomalous diffusion; Zeta functions; Weak chaos 1. Introduction In this paper we consider deterministic dynamical systems that exhibit nontrivial transport properties (which may be associated to either normal or anomalous diffusion). We start by dealing with the case of hyperbolic systems where typically normal diffusion is observed (even though actual calculation of transport coefficients may be exceedingly difficult [1,2]), while the in the second part we consider weakly chaotic systems, where long trappings near regular phase-space regions may induce anomalies in diffusive properties. 2. Normal diffusion A prototype model of diffusing system is realized via a chain of one-dimensional maps obtained by lifting a torus map on the whole real line (see Fig. 1). * Corresponding author. Address: Dipartimento di Scienze Chimiche, Fisiche e Matematiche, Istituto Nazionale di Fisica Nucleare, Sezione di Milan