Complexity reduction of C-algorithm
Classical Analysis and ODEs
2013-12-13 v2 Dynamical Systems
Abstract
The C-Algorithm introduced in [Chouikha2007] is designed to determine isochronous centers for Lienard-type differential systems, in the general real analytic case. However, it has a large complexity that prevents computations, even in the quartic polynomial case. The main result of this paper is an efficient algorithmic implementation of C-Algorithm, called ReCA (Reduced C-Algorithm). Moreover, an adapted version of it is proposed in the rational case. It is called RCA (Rational C-Algorithm) and is widely used in [BardetBoussaadaChouikhaStrelcyn2010] and [BoussaadaChouikhaStrelcyn2010] to find many new examples of isochronous centers for the Li\'enard type equation.
Keywords
Cite
@article{arxiv.1007.3653,
title = {Complexity reduction of C-algorithm},
author = {Magali Bardet and Islam Boussaada},
journal= {arXiv preprint arXiv:1007.3653},
year = {2013}
}