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Advances in Fractional Calculus pp 127–138Cite as

Fractional Kinetics in Pseudochaotic Systems and Its Applications

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The phenomenon of stickiness of the dynamical trajectories to the domains of periodic orbits (islands), or simply to periodic orbits, can be considered a primary source of the fractional kinetic equation (FKE). An additional condition for the FKE occurrence is a property of the corresponding sticky domains to have space-time invariance under the space-time renormalization transform. The dynamics in some class of polygonal billiards is pseudochaotic (i.e., dynamics is random but the Lyapunov exponent is zero), and the corresponding features of the self-similarity are reflected in the discrete space-time renormalization invariance. We consider an example of such a billiard and its dynamical and kinetic properties that leads to the FKE. Keywords Fractional kinetics, pseudochaos, recurrences, billiards.

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Authors and Affiliations

  1. Courant Institute of Mathematical Sciences and Department of Physics, New York University, Mercer Street, 251, 10012, New York, NY

    George M. Zaslavsky

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  1. George M. Zaslavsky
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Editors and Affiliations

  1. Université Bordeaux 1, – ENSEIRB, 351 cours de la Libération, F33405, Talence Cedex, France

    Jocelyn Sabatier

  2. Southern Illinois University, 62901, Carbondale, IL, USA

    Om Prakash Agrawal

  3. Institute of Engineering of Porto, Rua Dr. António Bernardino de Almeida, 4200-072, Porto, Portugal

    J. A. Tenreiro Machado

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Zaslavsky, G.M. (2007). Fractional Kinetics in Pseudochaotic Systems and Its Applications. In: Sabatier, J., Agrawal, O.P., Machado, J.A.T. (eds) Advances in Fractional Calculus. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6042-7_9

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  • DOI: https://doi.org/10.1007/978-1-4020-6042-7_9

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  • Print ISBN: 978-1-4020-6041-0

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