### Abstract

Original language | English |
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Pages (from-to) | 309-320 |

Number of pages | 12 |

Journal | Physics Letters A |

Volume | 266 |

Issue number | 4-6 |

DOIs | |

Publication status | Published - 28 Feb 2000 |

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*Physics Letters A*,

*266*(4-6), 309-320. https://doi.org/10.1016/S0375-9601(00)00032-3

**Fractal escapes in Newtonian and relativistic multipole gravitational fields.** / de Moura, Alessandro P. S.; Letelier, Patricio S.

Research output: Contribution to journal › Article

*Physics Letters A*, vol. 266, no. 4-6, pp. 309-320. https://doi.org/10.1016/S0375-9601(00)00032-3

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TY - JOUR

T1 - Fractal escapes in Newtonian and relativistic multipole gravitational fields

AU - de Moura, Alessandro P. S.

AU - Letelier, Patricio S.

PY - 2000/2/28

Y1 - 2000/2/28

N2 - We study the planar motion of test particles in gravitational fields produced by an external material halo. Both the Newtonian and the general-relativistic dynamics are examined, and in the relativistic case the dynamics of both massive and massless particles are investigated. The halo field is given in general by a multipole expansion; we restrict ourselves to multipole fields of pure order, whose Newtonian potentials are homogeneous polynomials in cartesian coordinates. A pure n-pole field has n different escapes, one of which is chosen by the particle according to its initial conditions. We find that the escape has a fractal dependency on the initial conditions for n>2 both in the Newtonian and the relativistic cases for massive test particles, but with important differences between them. The relativistic motion of massless particles, however, was found to be regular for all the fields we could study. The box-counting dimension was used in each case to quantify the sensitivity to initial conditions which arises from the fractality of the escape route.

AB - We study the planar motion of test particles in gravitational fields produced by an external material halo. Both the Newtonian and the general-relativistic dynamics are examined, and in the relativistic case the dynamics of both massive and massless particles are investigated. The halo field is given in general by a multipole expansion; we restrict ourselves to multipole fields of pure order, whose Newtonian potentials are homogeneous polynomials in cartesian coordinates. A pure n-pole field has n different escapes, one of which is chosen by the particle according to its initial conditions. We find that the escape has a fractal dependency on the initial conditions for n>2 both in the Newtonian and the relativistic cases for massive test particles, but with important differences between them. The relativistic motion of massless particles, however, was found to be regular for all the fields we could study. The box-counting dimension was used in each case to quantify the sensitivity to initial conditions which arises from the fractality of the escape route.

U2 - 10.1016/S0375-9601(00)00032-3

DO - 10.1016/S0375-9601(00)00032-3

M3 - Article

VL - 266

SP - 309

EP - 320

JO - Physics Letters A

JF - Physics Letters A

SN - 0375-9601

IS - 4-6

ER -