# Isochronicity and linearizability of a planar cubic system

## TL;DR

This paper studies when certain cubic planar differential systems can be simplified to linear systems and explores conditions for isochronous centers, providing a classification based on system parameters.

## Contribution

It offers a classification of linearizable cubic systems and conditions for isochronous centers, advancing understanding of their dynamics.

## Key findings

- Derived parameter conditions for linearizability
- Identified coexistence criteria for isochronous centers
- Classified families of cubic systems based on linearizability

## Abstract

In this paper we investigate the problem of linearizability for a family of cubic complex planar systems of ordinary differential equations. We give a classification of linearizable systems in the family obtaining conditions for linearizability in terms of parameters. We also discuss coexistence of isochronous centers in the systems.