Controlling the stability of periodic orbits of completely integrable systems
Dynamical Systems
2015-03-04 v3 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.1311.1184,
title = {Controlling the stability of periodic orbits of completely integrable systems},
author = {Razvan M. Tudoran},
journal= {arXiv preprint arXiv:1311.1184},
year = {2015}
}
Comments
19 pages