Cycle Expansions for Intermittent Maps

Roberto Artuso, Predrag Cvitanović, Gregor Tanner
2003 Progress of Theoretical Physics Supplement  
In a generic dynamical system chaos and regular motion coexist side by side, in different parts of the phase space. The border between these, where trajectories are neither unstable nor stable but of marginal stability, manifests itself through intermittency, dynamics where long periods of nearly regular motions are interrupted by irregular chaotic bursts. We discuss the Perron-Frobenius operator formalism for such systems, and show by means of a 1-dimensional intermittent map that
more » ... induces branch cuts in dynamical zeta functions. Marginality leads to long-time dynamical correlations, in contrast to the exponentially fast decorrelations of purely chaotic dynamics. We apply the periodic orbit theory to quantitative characterization of the associated power-law decays.
doi:10.1143/ptps.150.1 fatcat:zjevxui46ncannqivc34eifchy