Abstract We characterize global centers (all solutions are periodic) of the piecewise linear equation x'=a (t) |x| + b (t) x ′ = 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' (t) a (t) = P (h (t) ) h ′ (t), b (t) =Q (h (t) ) h' (t) b (t) = Q (h (t) ) h ′ (t).
Bravo et al. (Fri,) studied this question.