Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 19, pp. 1-14.

Title: Piecewise linear differential systems with an algebraic line of separation

Authors: Armengol Gasull (Univ. Autonoma de Barcelona, Catalonia, Spain)
         Joan Torregrosa (Univ. Autonoma de Barcelona, Catalonia, Spain)
         Xiang Zhang (Shanghai Jiao Tong Univ., Shanghai, China)

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
 $n\in\mathbb{N}$ 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.
 
Submitted April 23, 2018. Published February 14, 2020.
Math Subject Classifications: 34C25, 34C07, 37G15.
Key Words: Piecewise linear differential system;
           algebraic separation; limit cycle; ECT-system.