Non isolated periodic orbits of a fixed period for quadratic dynamical systems

Abstract

Given a dynamical system in R 3 and γ τ a periodic orbit of period τ > 0, non isolated among periodic orbits of period τ (for any neighborhood V ⊂ R 3 of γ τ , there exist another periodic orbit γ τ ⊂ V of period τ), a way of obtaining non isolated periodic orbits of a fixed period τ for polynomial dynamical systems is emphasized. As an application, we build up a counter example to answer a referee's question.