Centers with equal period functions

TL;DR

This paper provides a sufficient condition for symmetric systems to have periodic solutions with equal periods, applicable to both Hamiltonian and non-Hamiltonian systems, and demonstrates this with planar centers.

Contribution

It introduces a new sufficient condition for equal period functions in symmetric systems, extending applicability to various types of dynamical systems.

Findings

Established a sufficient condition for equal period functions in symmetric systems

Applied the condition to construct planar centers with equal periods

Demonstrated applicability to both Hamiltonian and non-Hamiltonian systems

Abstract

We give a sufficient condition for systems with symmetries to have periodic solutions with equal periods. We show that the main result can be applied both to Hamiltonian and to non-Hamiltonian systems. We apply the main results to produce planar centers with equal period functions.