### 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 |
---|---|

Pages (from-to) | 697-704 |

Number of pages | 8 |

Journal | Progress of Theoretical Physics |

Volume | 10 |

Issue number | 4 |

Publication status | Published - 2001 Oct |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Progress of Theoretical Physics*,

*10*(4), 697-704.

**Dynamical systems that produce the Lévy flights.** / Miyaguchi, Tomoshige; Aizawa, Yoji.

Research output: Contribution to journal › Article

*Progress of Theoretical Physics*, vol. 10, no. 4, pp. 697-704.

}

TY - JOUR

T1 - Dynamical systems that produce the Lévy flights

AU - Miyaguchi, Tomoshige

AU - Aizawa, Yoji

PY - 2001/10

Y1 - 2001/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0035486619&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035486619&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0035486619

VL - 10

SP - 697

EP - 704

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 4

ER -