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Final comments

There are several questions of practical interest which could arise in connection with the non-integrability, such as the size of the chaotic zones (as it was established by Simó [8] in the J2-problem) and, in general, its relevance from a practical point of view. Most of these questions are still open and the answers do not seem to be trivial. Some considerations about the physical meaning of the orbits required by Ziglin's method, as well as some numerical simulations can be seen in [7], where it is shown the appearance of chaos (hard or soft) for moderate values of J22 in the neighbourhood of the 1:1 resonant orbit.