Periodic orbits of the Sitnikov problem via a Poincaré map

Montserrat Corbera; Jaume Llibre

doi:10.1023/A:1011117003713

Periodic orbits of the Sitnikov problem via a Poincaré map

Montserrat Corbera, Jaume Llibre

Departament de Matemàtiques

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Resum

In this paper by means of a Poincaré map, we prove the existence of symmetric periodic orbits of the elliptic Sitnikov problem. Furthermore, using the presence of the Bernoulli shift as a subsystem of that Poincaré map, we prove that not all the periodic orbits of the Sitnikov problem are symmetric periodic orbits.

Idioma original	Anglès
Pàgines (de-a)	273-303
Revista	Celestial Mechanics and Dynamical Astronomy
Volum	77
DOIs	https://doi.org/10.1023/A:1011117003713
Estat de la publicació	Publicada - 1 de gen. 2000

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@article{00275e1b966749a8965422f9f89670dc,

title = "Periodic orbits of the Sitnikov problem via a Poincar{\'e} map",

abstract = "In this paper by means of a Poincar{\'e} map, we prove the existence of symmetric periodic orbits of the elliptic Sitnikov problem. Furthermore, using the presence of the Bernoulli shift as a subsystem of that Poincar{\'e} map, we prove that not all the periodic orbits of the Sitnikov problem are symmetric periodic orbits.",

keywords = "Periodic orbits, Poincar{\'e} map, Sitnikov motions, Symmetric periodic orbits",

author = "Montserrat Corbera and Jaume Llibre",

year = "2000",

month = jan,

day = "1",

doi = "10.1023/A:1011117003713",

language = "English",

volume = "77",

pages = "273--303",

journal = "Celestial Mechanics and Dynamical Astronomy",

issn = "0923-2958",

}

TY - JOUR

T1 - Periodic orbits of the Sitnikov problem via a Poincaré map

AU - Corbera, Montserrat

AU - Llibre, Jaume

PY - 2000/1/1

Y1 - 2000/1/1

N2 - In this paper by means of a Poincaré map, we prove the existence of symmetric periodic orbits of the elliptic Sitnikov problem. Furthermore, using the presence of the Bernoulli shift as a subsystem of that Poincaré map, we prove that not all the periodic orbits of the Sitnikov problem are symmetric periodic orbits.

AB - In this paper by means of a Poincaré map, we prove the existence of symmetric periodic orbits of the elliptic Sitnikov problem. Furthermore, using the presence of the Bernoulli shift as a subsystem of that Poincaré map, we prove that not all the periodic orbits of the Sitnikov problem are symmetric periodic orbits.

KW - Periodic orbits

KW - Poincaré map

KW - Sitnikov motions

KW - Symmetric periodic orbits

U2 - 10.1023/A:1011117003713

DO - 10.1023/A:1011117003713

M3 - Article

SN - 0923-2958

VL - 77

SP - 273

EP - 303

JO - Celestial Mechanics and Dynamical Astronomy

JF - Celestial Mechanics and Dynamical Astronomy

ER -

Periodic orbits of the Sitnikov problem via a Poincaré map

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