THE LOCATION OF SECULAR RESONANCES CLOSE TO THE 2 1 COMMENSURABILITY/

This paper is devoted to the problem of the location of secular resona nces close to a mean motion commensurability in the main asteroid belt . This is quite a difficult problem because of the presence of several resonances in the same part of the phase space, which makes it a dyna mical system with strongly coupled degrees of freedom. Therefore, we a pply here the perturbation method of ''successive elimination of harmo nics'' in order to find out in the regular regions the proper frequenc ies of the system and, consequently, locate the secular resonances. In particular, we concentrate on the location of the nu6 resonance close to the 2/1 commensurability, since this is related to the existence o f the upper bound of the distribution of the inclinations of the aster oids between 3.0 and 3.2 A.U.. We confirm that, as suspected, the nu6 resonance is at a larger inclination than the main asteroid population . Our theoretical findings are confirmed by several numerical integrat ions, with initial conditions systematically chosen on a suitable grid .