arXiv:1311.1184 Abstract | arXiv Analytics

arXiv:1311.1184 [math.DS]Abstract References Reviews Resources

Controlling the stability of periodic orbits of completely integrable systems

Published 2013-11-05, updated 2014-09-23Version 3

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.

Comments: 19 pages

Categories: math.DS, math-ph, math.MP, nlin.SI

Keywords: periodic orbit, dissipative dynamical system, main results, general codimension, characteristic multipliers

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