Home > Articles > Published articles > Periods of solutions of periodic differential equations |
Date: | 2016 |
Abstract: | Smooth non-autonomous T-periodic differential equations x'(t)=f(t,x(t)) defined in \R\K^n, where \K is \R or \C and n 2 can have periodic solutions with any arbitrary period~S. We show that this is not the case when n=1. We prove that in the real C^1-setting the period of a non-constant periodic solution of the scalar differential equation is a divisor of the period of the equation, that is T/S\N. Moreover, we characterize the structure of the set of the periods of all the periodic solutions of a given equation. We also prove similar results in the one-dimensional holomorphic setting. In this situation the period of any non-constant periodic solution is commensurable with the period of the equation, that is T/S\Q. |
Grants: | Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-859 Ministerio de Economía y Competitividad MTM2013-40998-P Ministerio de Economía y Competitividad MTM2014-52209-C2-1-P |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Holomorphic differential equations ; Periodic differential equations ; Periodic orbit |
Published in: | Differential and Integral Equations. An International Journal for Theory & Applications, Vol. 29 Núm. 9-10 (2016) , p. 905-922, ISSN 0893-4983 |
Postprint 18 p, 318.6 KB |