Transversal homoclinic orbits in the collinear restricted three-body problem

被引：8

作者：

Llibre, J ^{[1
]}

Perez-Chavela, E

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain

[2] Univ Autonoma Metropolitana Iztapalapa, Dept Matemat, Mexico City 09340, DF, Mexico

来源：

JOURNAL OF NONLINEAR SCIENCE | 2005年 / 15卷 / 01期

关键词：

Melnikov method; homoclinic loop; McGehee coordinates;

D O I：

10.1007/s00332-004-0511-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using the perturbation method of Melnikov, we prove in a simple way the existence of transversal homoclinic points in the collinear restricted three-body problem. As a consequence we can embed a Bernoulli shift on a suitable cross section of the flow, showing easily that this problem possesses chaotic dynamics.

引用

页码：1 / 10

页数：10

共 50 条

[1] Transversal Homoclinic Orbits in the Collinear Restricted Three-Body Problem
J. Llibre
E. Perez-Chavela
[J]. Journal of Nonlinear Science, 2005, 15 : 1 - 10
[2] Periodic orbits of a collinear restricted three-body problem
Corbera, M
Llibre, J
[J]. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2003, 86 (02): : 163 - 183
[3] Periodic Orbits of a Collinear Restricted Three-Body Problem
Montserrat Corbera
Jaume Llibre
[J]. Celestial Mechanics and Dynamical Astronomy, 2003, 86 : 163 - 183
[4] STUDIES　OF　MELNIKOV　METHOD　AND　TRANSVERSAL　HOMOCLINIC　ORBITS　IN　THE　CIRCULAR　PLANAR　RESTRICTED　THREE－BODY　PROBLEM
朱如曾
向程
[J]. Applied Mathematics and Mechanics(English Edition), 1996, (12) : 1177 - 1187
[5] Numerical determination of homoclinic and heteroclinic orbits at collinear equilibria in the restricted three-body problem with oblateness
Kalantonis, VS
Douskos, CN
Perdios, EA
[J]. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2006, 94 (02): : 135 - 153
[6] Numerical Determination of Homoclinic and Heteroclinic Orbits at Collinear Equilibria in the Restricted Three-Body Problem with Oblateness
V. S. Kalantonis
C. N. Douskos
E. A. Perdios
[J]. Celestial Mechanics and Dynamical Astronomy, 2006, 94 : 135 - 153
[7] Homoclinic and heteroclinic orbits in the photogravitational restricted three-body problem
Papadakis, K. E.
[J]. ASTROPHYSICS AND SPACE SCIENCE, 2006, 302 (1-4) : 67 - 82
[8] Homoclinic and heteroclinic orbits in the photogravitational restricted three-body problem
K. E. Papadakis
[J]. Astrophysics and Space Science, 2006, 302 : 67 - 82
[9] Halo orbits around the collinear points of the restricted three-body problem
Ceccaroni, Marta
Celletti, Alessandra
Pucacco, Giuseppe
[J]. PHYSICA D-NONLINEAR PHENOMENA, 2016, 317 : 28 - 42
[10] Periodic orbits of the restricted three-body problem
Mathlouthi, S
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 350 (06) : 2265 - 2276

← 1 2 3 4 5 →