Period two implies chaos for a class of ODEs: a dynamical system approach

Abstract

The aim of this note is to set in the field of dynamical systems a recent theorem by Obersnel and Omari about the presence of periodic solutions of all periods for a class of scalar time-periodic first order differential equations without uniqueness, provided a subharmonic solution (and thus, for instance, a solution of period two) does exist. Indeed, making use of the Bebutov flow, we try to clarify in what sense the term "chaos" has to be understood and which dynamical features can be inferred for the system under analysis.