Abstract

We study the number of limit cycles of planar piecewise linear differential systems separated by a branch of an algebraic curve. We show that for each $ninmathbb{N}$ there exist piecewise linear differential systems separated by an algebraic curve of degree $n$ having $[n/2]$ hyperbolic limit cycles. Moreover, when $n=1,2,3$ we study in more detail the problem. In particular, for $n=2,3,$ considering a perturbation of a center and constructing examples with 4 and 5 limit cycles, respectively. These results are proved showing that the set of functions generating the first order averaged function associated to the problem is an extended complete Chebyshev system (ECT-system) in a suitable interval.