Pseudochaotic dynamics near global periodicity

Abstract In this paper, we study a piecewise linear version of kicked oscillator model: saw-tooth map. A special case of global periodicity, in which every phase point belongs to a periodic orbit, is presented. With few analytic results known for the corresponding map on torus, we numerically investigate transport properties and statistical behavior of Poincare recurrence time in two cases of deviation from global periodicity. A non-KAM behavior of the system, as well as subdiffusion and superdiffusion, are observed through numerical simulations. Statistics of Poincare recurrences shows Kac lemma is valid in the system and there is a relation between the transport exponent and the Poincare recurrence exponent. We also perform careful numerical computation of capacity, information and correlation dimensions of the so-called exceptional set in both cases. Our results show that the fractal dimension of the exceptional set is strictly less than 2 and that the fractal structures are unifractal rather than multifractal.

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