Complexity reduction of C-Algorithm

摘要

The C-Algorithm introduced in [5] 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 [1], [2] to find many new examples of isochronous centers for the Liénard type equation.