PIECEWISE LINEAR DIFFERENTIAL SYSTEMS WITH AN ALGEBRAIC LINE OF SEPARATION.

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 n E N there exist piecewise linear differential systems separated by an algebraic curve of degree n having [n/2] hyperbolic limit cycles. Moreover, when n = 2, 3, we study in more detail the problem, considering a perturbation of a center and constructing examples with 4 and 5 limit cycles, respectively. These results follow by proving that the set of functions generating the first order averaged function associated to the problem is an extended complete Chebyshev system in a suitable interval. [ABSTRACT FROM AUTHOR]