Iván Sánchez ( Universitat Autonoma de Barcelona)

Friday, June 14th, 2019. 4:00 p.m., Room 4-001.

**Title: Critical periods of reversible Darboux linearizable isochronous centers**

**Abstract:** A well-known problem in dynamical systems is the study of ciclicity, which aims to find the maximum number of limit cycles bifurcating from a center or a focus. An analogous problem to study the criticality of an isochronous center, this is the maximum number of oscillations of its period function when a perturbation is added to the system. These oscillations are the so-called critical periods. In this talk I will introduce the period function of a system of differential equations in the plane. Then, for small values of the degree n, I will present some reversible Darboux linearizable systems, which has allowed us to provide the maximum number of critical periods in a system of fixed degree n so far according to our knowledge.