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

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  • Xuhua Cheng
  • Zhikun She

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.

Suggested Citation

  • Xuhua Cheng & Zhikun She, 2015. "A Note on the Existence of a Smale Horseshoe in the Planar Circular Restricted Three-Body Problem," Abstract and Applied Analysis, Hindawi, vol. 2015, pages 1-8, March.
    • Handle: RePEc:hin:jnlaaa:965829
    DOI: 10.1155/2015/965829
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