Period functions and critical periods of piecewise linear system
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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. <i>Electronic Journal of Differential Equations, 2020</i>(79), pp. 1-12.
Rights
Attribution 4.0 International