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Forced quasi-periodic oscillations in strongly dissipative systems of any finite dimension. (arXiv:1710.01266v2 [math.DS] UPDATED)
来源于:arXiv
We consider a class of singular ordinary differential equations describing
analytic systems of arbitrary finite dimension, subject to a quasi-periodic
forcing term and in the presence of dissipation. We study the existence of
response solutions, i.e. quasi-periodic solutions with the same frequency
vector as the forcing term, in the case of large dissipation. We assume the
system to be conservative in the absence dissipation, so that the forcing term
is --- up to the sign --- the gradient of a potential energy, and both the mass
and damping matrices to be symmetric and positive definite. Further, we assume
a non-degeneracy condition on the forcing term, essentially that the
time-average of the potential energy has a strict local minimum. On the
contrary, no condition is assumed on the forcing frequency; in particular we do
not require any Diophantine condition. We prove that, under the assumptions
above, a response solution always exist provided the dissipation is strong
enough. This e 查看全文>>