Abstract
The paper studies the problem of approximate construction of eigenvalues and multipliers of linear (autonomous and periodic) Hamiltonian systems depending on a small parameter in the main critical cases. New formulas for the asymptotic (in powers of a small parameter) representation of the eigenvalues and multipliers of the task are proposed. The obtained formulas allow us to effectively study the problems of stability and hyperbolicity of linear systems, equilibrium points and periodic solutions of nonlinear Hamiltonian systems, the problem of constructing the boundaries of the regions of stability and hyperbolicity, problems of local bifurcations of nonlinear dynamical systems, etc.
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