Abstract
We investigate the fulfillment of the conditions for the application of the Nekhoroshev theorem to a real dynamical system, such as the motion of the asteroids under the perturbation of the major planets. We have in particular analysed the regions of the phase space where the asteroid families of Koronis and Veritas are located. The results obtained for some members of the selected families indicate that in these regions even stricter conditions (convexity, quasi-convexity and three-jet) than the condition of steepness required by the theorem are fulfilled. Consequently, the Nekhoroshev theorem can be applied to those members of the Koronis family and to the members of the Veritas family with a regular motion.
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