00-410 Michele V. Bartuccelli, Guido Gentile , Kyriakos V. Georgiou
Lindstedt series for perturbations of isochronous systems. II. KAM theorem and stability of the upside-down pendulum (293K, Postscript) Oct 18, 00
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Abstract. We consider the planar pendulum with support point oscillating in the vertical direction, and we study its motion around the equilibrium point corresponding to the upside-down position. We prove that the equilibrium point is stable for the projection of the motion on the pendulum phase space (for a full measure subset of the stability region of the linearized system inside the two-dimensional space of parameters), by proving the persistence of invariant KAM tori for the two-dimensional system describing the model.

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