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JOURNALS // Regular and Chaotic Dynamics // Archive

Regul. Chaotic Dyn., 2013 Volume 18, Issue 6, Pages 585–599 (Mi rcd150)

This article is cited in 6 papers

Stable Periodic Solutions in the Forced Pendulum Equation

Rafael Ortega

Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Abstract: Consider the pendulum equation with an external periodic force and an appropriate condition on the length parameter. It is proved that there exists at least one stable periodic solution for almost every external force with zero average. The stability is understood in the Lyapunov sense.

Keywords: Lyapunov stability, forced pendulum, prevalence, periodic solution, regular value, discriminant.

MSC: 34D20, 34C15, 34C25, 37C25, 58K05

Received: 15.05.2013
Accepted: 04.10.2013

Language: English

DOI: 10.1134/S1560354713060026



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