**35th Meeting of the AAS Division on Dynamical Astronomy, April 2004**

*Session 4 Posters I*

, Wednesday, April 21, 2004, 7:00-8:30pm,
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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.