Stable periodic solutions in the forced pendulum equation [ Back ]

Date:
10.06.13   
Times:
15:30 to 16:30
Place:
UAB - Dept. Matemàtiques (C1/-128)
Speaker:
Rafael Ortega
University:
Universidad de Granada

Abstract:

Consider the equation $$x''+\beta \sin x=f(t)$$ where the forcing is $2\pi$-periodic and satisfies $$ \int_0^{2\pi} f(t)dt =0.$$ I present the following result: assuming $0<\beta <1/4$, for almost every forcing there exists a stable $2\pi$-periodic solution. The sentence “for almost every forcing” is understood in the sense of prevalence and is needed, the result is false for some forcings. The number 1/4 is sharp.