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

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

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It has been proved that, in the classical planar circular restricted three-body problem, Quilt Patterns 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 Vacuums the existence of a Smale horseshoe in this classical restricted three-body problem.