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DCDS

We consider second-order Euler-Lagrange systems which are periodic in time. Their periodic solutions may be characterized as the
stationary points of an associated action functional, and we
study the dynamical implications of minimizing the action.
Examples are well-known of stable periodic minimizers, but
instability always holds for periodic solutions which are minimal in the sense of
Aubry-Mather.

PROC

Please refer to Full Text.

DCDS

We consider planar systems driven by a central force which depends periodically on time. If the force is sublinear and attractive, then there is a connected set of subharmonic and quasi-periodic solutions rotating around the origin at different speeds; moreover, this connected set stretches from zero to infinity. The result still holds allowing the force to be attractive only in average provided that an uniformity condition is satisfied and there are no periodic oscillations with zero angular momentum. We provide examples showing that these assumptions cannot be skipped.

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