Electron. J. Differential Equations, Vol. 2020 (2020), No. 79, pp. 112.
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 nonnegative integers
,
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
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.
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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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