Periods of solutions of periodic differential equations
Cimà, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

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

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