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[4.08] The full spectrum of Lyapunov Characteristic Numbers and its relation to the existence of Local Integrals of Motion

H. Varvoglis (University of Thessaloniki)

In a recent paper [1] we estimated the topological dimension of trajectories belonging to three typical classes of the Restricted Three Body Problem (RTBP), namely regular, chaotic and stable chaotic. We found that stable chaotic trajectories seem to wonder in a phase space region where local integrals of motion exist, besides the already known isolating integral of the Hamiltonian in the extended phase space. In the present work we calculate the full spectrum of Lyapunov Characteristic Numbers (LCN) of trajectories belonging to the above-mentioned typical classes and we compare our results to the topological structure of the phase space implied by the existence or not of local integrals of motion.

[1] H. Varvoglis, K. Tsiganis and G. Hadjivantsides, Stable chaos and local integrals of motion, in Proceedings of the Conference Asteroids, Comets, Meteors - ACM2002, 29 July-2 August 2002, Technical University Berlin, ed. by B. Warmbein (ESA SP-500, 2002), pp. 355-357

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Bulletin of the American Astronomical Society, 36 #2
© 2004. The American Astronomical Soceity.