Chaotic motion and the Graziani-Black criterion

Astronomy and Astrophysics – Astronomy

Scientific paper

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Chaos, Hill Method, Laplace Equation, Liapunov Functions, Three Body Problem, Gravitational Effects, Planetary Evolution, Poincare Problem, Star Clusters

Scientific paper

Chaotic motion is presented as a fundamental cause for the development of the Laplacian instability described by the Graziani-Black (GB) criterion. While the GB criterion is valid for different sets of finite masses in a general three-body system, a circular planar restricted three-body system is studied here. Poincare surfaces of section and Liapunov characteristic numbers are used to test for the chaotic motion in this system. A simple description of the chaos detection techniques and the GB criterion is provided.

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