### Abstract

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.

Original language | English |
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Pages (from-to) | 697-704 |

Number of pages | 8 |

Journal | Progress of Theoretical Physics |

Volume | 10 |

Issue number | 4 |

Publication status | Published - 2001 Oct |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

Miyaguchi, T., & Aizawa, Y. (2001). Dynamical systems that produce the Lévy flights.

*Progress of Theoretical Physics*,*10*(4), 697-704.