Dynamical Systems That Produce the Levy Flights.

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  • Miyaguchi Tomoshige
    Department of Applied Physics, Faculty of Science and Engineering Waseda University, Tokyo 169-8555, Japan
  • Aizawa Yoji
    Department of Applied Physics, Faculty of Science and Engineering Waseda University, Tokyo 169-8555, Japan

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Description

We introduce a one-dimensional map producing flights of arbitrary length and explain that the orbits and the density functions that evolve under this map have the same properties as Lévy flight. We derive an approximated Frobenius-Perron equation and prove that this equation converges to the Lévy diffusion equation.

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