Cycle expansions for intermittent maps

Details Cycle expansions for intermittent maps Cycle expansions for intermittent maps

2003-05-07

arxiv.org/abs/nlin/0305008v2

Nonlinear Sciences

Chaotic Dynamics

22 pages, 5 figures

Scientific paper

10.1143/PTPS.150.1

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 intermittency 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.

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