ARNOLD DIFFUSION AND OSCILLATORY SOLUTIONS IN THE PLANAR 3-BODY PROBLEM

被引：28

作者：

XIA, Z

机构：

[1] Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 1994年 / 110卷 / 02期

关键词：

D O I：

10.1006/jdeq.1994.1069

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the following results concerning the Newtonian three-body problem are obtained: (1) Arnold diffusion exists in the planar three-body problem, as conjectured by V. 1. Arnold (1964, Dokl. Acad. Nauk SSSR 156, 9). (2) The Oscillatory solutions as well as capture and escaping solutions, among other classes of chaotic solutions, exist in the three-body problem. (3) A special and interesting phenomenon, which we call the pseudo Arnold diffusion, arises near infinity in the three-body problem. (4) As a result of the existence of Arnold diffusion, the planar three-body problem is non-integrable and there are no additional real analytic integrals besides the known ones. (C) 1994 Academic Press, Inc.

引用

页码：289 / 321

页数：33

共 24 条

[1]

Alekseev V M., 1968, MATH USSR SB, V6, P505, DOI [10.1070/SM1968v006n04ABEH001074, DOI 10.1070/SM1968V006N04ABEH001074]

[2]

ALEKSEEV VM, 1968, MATH USSR SB, V5, P73

[3]

[Anonymous], [No title captured]

[4]

Arnol'd V. I., 1988, ENCY MATH SCI, V3

[5]

ARNOLD VI, 1964, DOKL AKAD NAUK SSSR+, V156, P9

[6]

ARNOLD VI, 1965, CR HEBD ACAD SCI, V26, P3719

[7]

Chirikov BV, 1979, PHYS REP, V52, P265

[8]

EASTON R, IN PRESS CELESTIAL M

[9] PARABOLIC ORBITS IN THE PLANAR 3 BODY PROBLEM [J].

EASTON, RW .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1984, 52 (01) :116-134

[10] HOMOCLINIC PHENOMENA FOR ORBITS DOUBLY ASYMPTOTIC TO AN INVARIANT 3-SPHERE [J].

EASTON, RW ;

MCGEHEE, R .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1979, 28 (02) :211-240

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