# The theory of the weak centers

Date:
20.01.20
Times:
15:30
Place:
UAB - Dept. Matemàtiques (C1/-128)
Speaker:
Valentí Ramírez
University:
Universitat Autònoma de Barcelona

Abstract:

This talk is dedicated to study the subclass of linear type centers which we call the {\it weak centers}. We say that the linear type center is a weak center if the Poincare-Liapunov first integral can be written as $H=(x^2 +y^2)/2(1+h.o.t.).$

We have characterized the expression of an analytic (polynomial) differential systems having  a weak center. We prove that the uniform and holomorphic centers are weak centers. Moreover we give the conjecture that all the weak centers are quasi Darboux integrable. Finally we established the relations between a particular case of weak centers and reversibility.