Period functions and critical periods of piecewise linear system

Date

2020-07-27

Authors

Wang, Shaoqing
Yang, Jiazhong

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

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 n₁, n₂, ..., nₘ, 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 n₁, n₂, ..., nₘ critical periods. Moreover, an algebraic curve can be chosen as the separation line in system of the first type.

Description

Keywords

Piecewise linear system, Period annulus, Period function, Critical period

Citation

Wang, S., & Yang, J. (2020). Period functions and critical periods of piecewise linear system. Electronic Journal of Differential Equations, 2020(79), pp. 1-12.

Rights

Attribution 4.0 International

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