A Note on the Existence of a Smale Horseshoe in the Planar Circular Restricted Three-Body Problem

Xuhua Cheng and Zhikun She

Abstract and Applied Analysis, 2015, vol. 2015, 1-8

Abstract:

It has been proved that, in the classical planar circular restricted three-body problem, the degenerate saddle point processes transverse homoclinic orbits. Since the standard Smale-Birkhoff theorem cannot be directly applied to indicate the chaotic dynamics of the Smale horseshoe type, we in this note alternatively apply the Conley-Moser conditions to analytically prove the existence of a Smale horseshoe in this classical restricted three-body problem.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:965829

DOI: 10.1155/2015/965829

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