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Author:

Cheng, Xuhua (Cheng, Xuhua.) | She, Zhikun (She, Zhikun.)

Indexed by:

EI Scopus SCIE

Abstract:

In this paper, the chaotic behavior of a planar restricted four-body problem with an equilateral triangle configuration is analytically studied. Firstly, according to the perturbation method of Melnikov, the planar restricted four-body problem is regarded as a perturbation of the two-body model. Then, we show that the Melnikov integral function has a simple zero, arriving at the existence of transversal homoclinic orbits. Afterwards, since the standard Smale-Birkhoff homoclinic theorem cannot be directly applied to the case of a degenerate saddle, we alternatively construct an invertible map f and check that f is a Smale horseshoe map, showing that our restricted four-body problem possesses chaotic behavior of the Smale horseshoe type.

Keyword:

Melnikov method transversal homoclinic orbits Chaotic behavior the restricted four-body problem Smale horseshoe

Author Community:

  • [ 1 ] [Cheng, Xuhua]Tsinghua Univ, Dept Math Sci, Zhongguancun St, Beijing 100084, Peoples R China
  • [ 2 ] [Cheng, Xuhua]Beijing Univ Technol, Gengdan Inst, Dept Math & Phys, Beijing 101300, Peoples R China
  • [ 3 ] [She, Zhikun]Beihang Univ, LMIB, Xueyuan Rd 37, Beijing 100191, Peoples R China
  • [ 4 ] [She, Zhikun]Beihang Univ, Sch Math & Syst Sci, Xueyuan Rd 37, Beijing 100191, Peoples R China

Reprint Author's Address:

  • [She, Zhikun]Beihang Univ, LMIB, Xueyuan Rd 37, Beijing 100191, Peoples R China;;[She, Zhikun]Beihang Univ, Sch Math & Syst Sci, Xueyuan Rd 37, Beijing 100191, Peoples R China

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Source :

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

ISSN: 0218-1274

Year: 2017

Issue: 2

Volume: 27

2 . 2 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

ESI HC Threshold:66

CAS Journal Grade:3

Cited Count:

WoS CC Cited Count: 9

SCOPUS Cited Count: 11

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 0

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