Pseudochaotic dynamics near global periodicity |
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| Institution: | 1. Department of Physics, New York University, 2-4 Washington Place, New York, NY 10003, USA;2. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA;1. School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2PB, United Kingdom;2. Faculty of Engineering, University of Nottingham, Nottingham, NG7 2PB, United Kingdom;1. School of Mathematics, Statistics & Actuarial Science, University of Kent, Canterbury, UK;2. School of Mathematics, University of Leeds, Leeds, UK;1. School of Mathematics and Statistics, University of New South Wales, Australia;2. School of Mathematics and Statistics, University of Sydney, Australia;3. School of Mathematical Sciences, Monash University, Australia;1. Organization for the Strategic Coordination of Research and Intellectual Property, Meiji University, Kawasaki 214-8571, Japan;2. Department of Electronics and Bioinformatics, Meiji University, Kawasaki 214-8571, Japan;3. Department of Mechanical and Energy System Engineering, Oita University, Oita 870–1192, Japan;1. Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, 20133 Milano, Italy;2. Departement of Mathematics and Namur Center for Complex Systems - naXys, University of Namur, 8 Rempart de la Vierge, B5000 Namur, Belgium |
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| 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 Poincaré 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 Poincaré recurrences shows Kac lemma is valid in the system and there is a relation between the transport exponent and the Poincaré 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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