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Controlling the stability of periodic orbits of completely integrable systems (1311.1184v3)
Published 5 Nov 2013 in math.DS, math-ph, math.MP, and nlin.SI
Abstract: We provide a constructive method designed in order to control the stability of a given periodic orbit of a general completely integrable system. The method consists of a specific type of perturbation, such that the resulting perturbed system becomes a codimension-one dissipative dynamical system which also admits that orbit as a periodic orbit, but whose stability can be a-priori prescribed. The main results are illustrated in the case of a three dimensional dissipative perturbation of the harmonic oscillator, and respectively Euler's equations form the free rigid body dynamics.
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