Cycle expansions for intermittent maps

Abstract

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.

22 pages, 5 figures

References in corpus (2)

• Stability ordering of cycle expansions
• Complete Determination of the Spectrum of a Transfer Operator associated with Intermittency

Cited by in corpus (9)

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• Anomalous transport: a deterministic approach
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• Fractal diffusion coefficient from dynamical zeta functions
• Wielding Intermittency with Cycle Expansions
• Accelerating cycle expansions by dynamical conjugacy
• Asymptotic expansions for the escape rate of stochastically perturbed unimodal maps
• Does an intermittent dynamical system remain (weakly) chaotic after drilling in a hole?