Reducible problem for a class of almost-periodic non-linear Hamiltonian systems

oleh: Muhammad Afzal, Tariq Ismaeel, Muhammad Jamal

Format: Article
Diterbitkan: SpringerOpen 2018-07-01

Deskripsi

Abstract This paper studies the reducibility of almost-periodic Hamiltonian systems with small perturbation near the equilibrium which is described by the following Hamiltonian system: dxdt=J[A+εQ(t,ε)]x+εg(t,ε)+h(x,t,ε). $$\frac{dx}{dt} = J \bigl[{A} +\varepsilon{Q}(t,\varepsilon) \bigr]x+ \varepsilon g(t,\varepsilon)+h(x,t,\varepsilon). $$ 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.