Period functions and critical periods of piecewise linear system

Abstract

n 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.
 For more information see https://ejde.math.txstate.edu/Volumes/2020/79/abstr.html