A note on the period function for certain planar vector fields

作者：Garijo Antonio; Gasull Armengol; Jarque Xavier^*

来源：Journal of Difference Equations and Applications, 2010, 16(5-6): 631-645.

DOI：10.1080/10236190903241689

• meromorphic vector fields
• periodic orbit
• period function
• critical period

Consider a smooth planar autonomous differential equation having a period annulus, P. We present a new criterion to ensure that the period function has at most one critical period on P. Our result has a compact form when the differential equation is written as (z) over dot = F(z,(z) over bar) It is based on a suitable representation formula of the derivative of the period function which uses the infinitesimal generator associated to the continua of periodic orbits. We apply the criterion to several particular cases of the equation (z) over dot = f(z)g((z) over bar)/h(z, (z) over bar) where f(z) and g((z) over bar) are holomorphic functions and h is a C(2) smooth real valuated function.

• 出版日期2010