Isochronicity conditions for some planar polynomial systems

TL;DR

This paper investigates conditions for isochronicity in planar polynomial systems, utilizing the C-algorithm to identify 27 new multiparameter isochronous centers, advancing understanding of center dynamics in differential equations.

Contribution

The paper introduces new isochronicity conditions for polynomial systems and discovers 27 previously unknown multiparameter isochronous centers using the C-algorithm.

Findings

Identified 27 new multiparameter isochronous centers.

Developed conditions for isochronicity in polynomial systems.

Applied the C-algorithm to analyze center behavior.

Abstract

We study the isochronicity of centers at $O\in \mathbb{R}^2$ for systems $\dot x=-y+A(x,y), \dot y=x+B(x,y)$, where $A, B\in \mathbb{R}[x,y]$, which can be reduced to the Lienard type equation. Using the so-called C-algorithm we have found 27 new multiparameter isochronous centers.