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 subharmonic solutions of all orders for a class of scalar time-periodic first order differential equations without uniqueness, provided a subharmonic solution (for instance, of order 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
Pireddu, M. (2009). Period two implies chaos for a class of ODEs: a dynamical system approach. RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE, 41, 43-54.
Period two implies chaos for a class of ODEs: a dynamical system approach
PIREDDU, MARINA
2009
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 subharmonic solutions of all orders for a class of scalar time-periodic first order differential equations without uniqueness, provided a subharmonic solution (for instance, of order 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
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