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, issue 1

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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https://doi.org/10.1155/2015/965829

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:965829

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