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Abstract
We numerically investigate the dynamics of a symmetric rigid body with a
fixed point in a small analytic external potential (equivalently, a fast
rotating body in a given external field) in the light of previous
theoretical investigations based on Nekhoroshev theory. Special
attention is posed on "resonant" motions, for which the tip of the
unit vector $\mu$ in the direction of the angular momentum vector can
wander, for no matter how small $\varepsilon$, on an extended, essentially
two-dimensional, region of the unit sphere, a phenomenon called "slow
chaos". We produce numerical evidence that slow chaos actually takes
place in simple cases, in agreement with the theoretical prediction.
Chaos however disappears for motions near proper rotations
around the symmetry axis, thus indicating that the theory of these
phenomena still needs to be improved. An heuristic explanation is
proposed.
Mathematics Subject Classification: 70E17, 65P10, 37J40.
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