Abstract
A non-autonomous periodic Hamiltonian system with one degree of freedom is studied in the neighbourhood of an elliptical equilibrium point. A uniform approximation of the solution in a finite time interval in the resonance case is determined using the projection method, instead of the traditional perturbation theoretical method. The Cauchy problem is reduced to a functional equation in the space of the derivatives, and a Galerkin scheme is constructed for this equation. A theorem is proved on convergence of the sequence of approximations to the exact solution. Every finite-dimensional approximation of sufficiently high order may be found by explicit iterations. The results can be generalized to dynamical systems of higher dimensions.
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