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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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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