# Period functions and critical periods of piecewise linear system

 dc.contributor.author Wang, Shaoqing dc.contributor.author Yang, Jiazhong dc.date.accessioned 2021-10-04T14:01:02Z dc.date.available 2021-10-04T14:01:02Z dc.date.issued 2020-07-27 dc.description.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. dc.description.department Mathematics dc.format Text dc.format.extent 12 pages dc.format.medium 1 file (.pdf) dc.identifier.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. dc.identifier.issn 1072-6691 dc.identifier.uri https://hdl.handle.net/10877/14586 dc.language.iso en dc.publisher Texas State University, Department of Mathematics dc.rights Attribution 4.0 International dc.rights.uri https://creativecommons.org/licenses/by/4.0/ dc.source Electronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas. dc.subject Piecewise linear system dc.subject Period annulus dc.subject Period function dc.subject Critical period dc.title Period functions and critical periods of piecewise linear system dc.type Article

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