Electron. J. Differential Equations, Vol. 2020 (2020), No. 79, pp. 1-12.

Period functions and critical periods of piecewise linear system

Shaoqing Wang, Jiazhong Yang

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 $n_1,n_2,\ldots,n_m$ 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.
DOI: 10.58997/ejde.2020.79

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Shaoqing Wang
School of Mathematical Sciences
Peking University
Beijing 100871, China
email: wangshaoqing@pku.edu.cn
Jiazhong Yang
School of Mathematical Sciences
Peking University
Beijing 100871, China
email: jyang@math.pku.edu.cn

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