On the existence of periodic orbits for the fixed homogeneous circle problem

C. Azevêdo; P. Ontaneda

doi:10.1016/j.jde.2006.12.012

On the existence of periodic orbits for the fixed homogeneous circle problem

C. Azevêdo
, P. Ontaneda

Mathematics and Statistics

Binghamton University

State University of New York Binghamton University

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and very near the homogeneous circle, as well as eight and spiral periodic orbits.

Original language	English
Pages (from-to)	341-365
Number of pages	25
Journal	Journal of Differential Equations
Volume	235
Issue number	2
DOIs	https://doi.org/10.1016/j.jde.2006.12.012
State	Published - Apr 15 2007

Keywords

Circle problem
Figure eight periodic orbit

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10.1016/j.jde.2006.12.012

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title = "On the existence of periodic orbits for the fixed homogeneous circle problem",

abstract = "We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and very near the homogeneous circle, as well as eight and spiral periodic orbits.",

keywords = "Circle problem, Figure eight periodic orbit",

author = "C. Azev{\^e}do and P. Ontaneda",

year = "2007",

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T1 - On the existence of periodic orbits for the fixed homogeneous circle problem

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AU - Ontaneda, P.

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Y1 - 2007/4/15

N2 - We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and very near the homogeneous circle, as well as eight and spiral periodic orbits.

AB - We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and very near the homogeneous circle, as well as eight and spiral periodic orbits.

KW - Circle problem

KW - Figure eight periodic orbit

UR - https://www.scopus.com/pages/publications/33847738476

U2 - 10.1016/j.jde.2006.12.012

DO - 10.1016/j.jde.2006.12.012

M3 - Article

SN - 0022-0396

VL - 235

SP - 341

EP - 365

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 2

ER -

On the existence of periodic orbits for the fixed homogeneous circle problem

Abstract

Keywords

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