Abstract
Weconsider the planar pendulum with support point oscillating in thevertical direction; the upside-down position of the pendulumcorresponds to an equilibrium point for the projection of themotion on the pendulum phase space. By using the Lindstedt seriesmethod recently developed in literature starting from thepioneering work by Eliasson, we show that such an equilibriumpoint is stable for a full measure subset of the stability regionof the linearized system inside the two-dimensional space ofparameters, by proving the persistence of invariant KAM tori forthe two-dimensional Hamiltonian system describing the model.
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