On the control of stability of periodic orbits of completely integrable systems

Răzvan M. Tudoran

doi:10.3934/jgm.2015.7.109

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2015, Volume 7, Issue 1: 109-124. Doi: 10.3934/jgm.2015.7.109

This issue Previous Article Higher-order variational calculus on Lie algebroids Next Article

On the control of stability of periodic orbits of completely integrable systems

Răzvan M. Tudoran^1,

1.
The West University of Timişoara, Faculty of Mathematics and C.S., Department of Mathematics, B-dul. Vasile Pârvan, No. 4, 300223 - Timişoara

Received: January 31, 2014

Revised: December 31, 2014

Published: February 2015

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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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Mathematics Subject Classification: Primary: 37C27, 37C75; Secondary: 34C25.

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