Global Centers in Piecewise linear Differential Equations in the Cylinder

Abstract

We characterize global centers (all solutions are periodic) of the piecewise linear equation $x^{\prime }=a(t)|x|+b(t)$ when the coefficients $a,b$ are trigonometric polynomials, under some generic hypotheses. We prove that the global centers are those determined by the composition condition on $a,b$. That is, the equation has a global center if and only if there exist polynomials $P,Q$ and a trigonometric polynomial $h$ such that $a(t)=P(h(t))h^{\prime }(t)$, $b(t)=Q(h(t))h^{\prime }(t)$.

12 Pages, no figures

References in corpus (1)

• Vanishing Abelian integrals on zero-dimensional cycles