Study of the period function of a biparametric family of centers [ Back ]

15:30 to 16:30
UAB - Dept. Matemàtiques (C1/-128)
David Rojas
Universitat Autònoma de Barcelona


In this talk we study the behaviour of the period function for the biparametric family $x'=-y, y'=(1+x)^p-(1+x)^q.$ A critical point of a planar vector field is a center if it has a punctured neighbourhood that consists entirely of periodic orbits surrounding it. The largest neighbourhood with this property is called period annulus, and the period function is the function that assigns to each periodic orbit of the period annulus its period. This family has a center at $x=0$ for all the parameters and we study monotonicity, isochronicity and bifurcation of critical periods from the center and from the period annulus. We also present some general results about the value of the period function on the outer boundary.