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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.
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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