Cyclicity of Rigid Centers on Center Manifolds of Three-dimensional systems

TL;DR

This paper investigates the cyclicity of rigid centers in three-dimensional polynomial systems, providing new lower bounds and an example of bifurcating multiple limit cycles using Lyapunov constants.

Contribution

It introduces a novel lower bound of 13 limit cycles for quadratic rigid centers in three-dimensional systems using Lyapunov constants.

Findings

Lower bounds for cyclicity of rigid centers established

Example of bifurcating 13 limit cycles from a quadratic rigid center

Methodology based on Lyapunov constants

Abstract

We work with polynomial three-dimensional rigid differential systems. Using the Lyapunov constants, we obtain lower bounds for the cyclicity of the known rigid centers on their center manifolds. Moreover, we obtain an example of a quadratic rigid center from which is possible to bifurcate 13 limit cycles, which is a new lower bound for three-dimensional quadratic systems.