Fractional Zaslavsky and Henon Discrete Maps

Abstract

This paper is devoted to the memory of Professor George M. Zaslavsky passed away on November 25, 2008. In the field of discrete maps, George M. Zaslavsky introduced a dissipative standard map which is called now the Zaslavsky map. G. Zaslavsky initialized many fundamental concepts and ideas in the fractional dynamics and kinetics. In this paper, starting from kicked damped equations with derivatives of non-integer orders we derive a fractional generalization of discrete maps. These fractional maps are generalizations of the Zaslavsky map and the Henon map. The main property of the fractional differential equations and the correspondent fractional maps is a long-term memory and dissipation. The memory is realized by the fact that their present state evolution depends on all past states with special forms of weights.

26 pages, LaTeX

References in corpus (4)

• Fractional Equations of Kicked Systems and Discrete Maps
• Differential Equations with Fractional Derivative and Universal Map with Memory
• Long-term memory contribution as applied to the motion of discrete dynamical systems
• Superdiffusion in the Dissipative Standard Map

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• Trends, Directions for Further Research, and Some Open Problems of Fractional Calculus
• General Fractional Dynamics
• Fractional Dynamics with Non-Local Scaling
• Predator-prey models with memory and kicks: Exact solution and discrete maps with memory
• From Fractional Differential Equations with Hilfer Derivatives: To Discrete Maps with Memory
• Asymptotic cycles in fractional generalizations of multidimensional maps