07-58 Marian Gidea, Frederick Deppe, Gregory Anderson.

Phase space reconstruction in the restricted three-body problem (882K, pdf) Mar 9, 07

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Abstract. We study the motion of the infinitesimal mass in the planar circular restricted three-body problem. The infinitesimal mass can undergo regular or chaotic motions. It can be captured by one of the primaries, it can make transfers from one primary to another, or it can even escape those captures. We analyze through statistical methods the time-series given by the time intervals between successive crossings made by the infinitesimal particle to a given Poincar section. We apply Takens/Yorke embedding theory to reconstruct the phase space from these time series, and we use the correlation dimension of the reconstructed phase space as a tool to distinguish between various types of motions.

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