Electronic Journal of Differential Equations (Jul 2020)

Period functions and critical periods of piecewise linear system

  • Shaoqing Wang,
  • Jiazhong Yang

Journal volume & issue
Vol. 2020, no. 79,
pp. 1 – 12

Abstract

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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.

Keywords