The Basic Propositions of the Theory of λ-Zones of Stability of a Canonical System of Linear Differential Equations with Periodic Coefficients

Let S be a mechanical system with m degrees of freedom whose Hamiltonian H has the form $$H=\frac{1}{2}_\textrm{j},\sum_{\mathrm{k}=1}^{\mathrm{2m}}\mathrm{h_{jk}}(\omega \mathrm{t})\mathrm{x_jx_k}+\mathrm{f(t)},$$ where x1,...,xm are generalized coordinates, xm + 1,...,x2m are the corresponding generalized momenta of S, hjk(t) = hkj(t) (j,k = 1,...,m) are periodic functions of period T in the time variable t, and ω is a parameter.