Abstract
The stability of the steady motions of multiparametric systems is investigated for the critical case of N pairs of purely imaginary roots when several internal fourth-order resonances interact with each other. The earlier investigations (see the survey /1/) covered only the interaction of odd-order resonances. In general, the problem of stability when there are even-order resonances is more complicated; even in the case of the simplest, single fourth-order resonance there is no algebraic criterion of stability /2/.
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