Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 79, pp. 1-12.

Title: Period functions and critical periods of piecewise linear system
       
Authors: Shaoqing Wang (Peking Univ., Beijing, China)
         Jiazhong Yang (Peking Univ., Beijing, China)

Abstract:
 In this article, we study a rich and complex phenomena of planar piecewise linear
 systems having two domains of which the separation curves are not straight.
 We show that for  positive integers n and m and non-negative integers
 $n_1,n_2,\ldots,n_m$, there exist two types of piecewise linear systems:
 one has a period annulus possessing exactly n critical periods;
 the other has m period annuli possessing exactly $n_1,n_2,\dots,n_m$
 critical periods.
 Moreover, an algebraic curve can be chosen as the separation line in system of the
 first type.
 
Submitted June 22, 2020. Published July 27, 2020.
Math Subject Classifications: 34C05, 34C25, 34C27.
Key Words: Piecewise linear system; period annulus; period function; critical period.