Reducible problem for a class of almost-periodic non-linear Hamiltonian systems
Tóm tắt
This paper studies the reducibility of almost-periodic Hamiltonian systems with small perturbation near the equilibrium which is described by the following Hamiltonian system:
$$\frac{dx}{dt} = J \bigl[{A} +\varepsilon{Q}(t,\varepsilon) \bigr]x+ \varepsilon g(t,\varepsilon)+h(x,t,\varepsilon). $$
It is proved that, under some non-resonant conditions, non-degeneracy conditions, the suitable hypothesis of analyticity and for the sufficiently small ε, the system can be reduced to a constant coefficients system with an equilibrium by means of an almost-periodic symplectic transformation.
Tài liệu tham khảo
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