Abstract
A relation between nonintegrability of nonlinear dynamical systems with a continuous Fourier spectrum and irreversibility is investigated in terms of the Liealgebraic formalism. Résibois and Prigogine's singular invariants of motion play an essential role. As an application of the formalism, we solve the restricted three-body problem for the case of nearly parabolic motion of the third body. This gives a model of the motion of a comet in the solar system. The results indicate that there is (deterministic) chaos in the motion of a comet in a nearly parabolic orbit. A possible physical implication of the chaotic motion is the existence of a cometary cloud surrounding the solar system. The theoretical results are compared with numerical results, and show good agreement.
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Petrosky, T.Y. The cometary cloud in the solar system and the Résibois-Prigogine singular invariants of motion. J Stat Phys 48, 1363–1372 (1987). https://doi.org/10.1007/BF01009550
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DOI: https://doi.org/10.1007/BF01009550