Center boundaries for planar piecewise-smooth differential equations with two zones
Buzzi, Claudio. (Universidade Estadual Paulista (Brasil). Department of Mathematics)
Pazim, Rubens (Universidade Federal de Mato Grosso (Brasil). Inst. de Ciências Naturais Humanas e Sociais)
Pérez-González, Set (Universidade Estadual Paulista (Brasil). Department of Mathematics)

Date:	2017
Abstract:	This paper is concerned with 1-parameter families of periodic solutions of piecewise smooth planar vector fields, when they behave like a center of smooth vector fields. We are interested in finding a separation boundary for a given pair of smooth systems in such a way that the discontinuous system, formed by the pair of smooth systems, has a continuum of periodic orbits. In this case we call the separation boundary as a center boundary. We prove that given a pair of systems that share a hyperbolic focus singularity p 0 , with the same orientation and opposite stability, and a ray Σ 0 with endpoint at the singularity p 0 , we can find a smooth manifold Ω such that Σ 0 ∪ p 0 ∪ Ω is a center boundary. The maximum number of such manifolds satisfying these conditions is five. Moreover, this upper bound is reached.
Grants:	European Commission 318999
Note:	Agraïments: The first author is partially supported by Procad-Capes88881.068462/2014-01 and FAPESP2013/24541-0. The second author is partially supported by program CAPES/PDSE grant number 7038/2014-03 and CAPES/DS program number 33004153071P0. The third author is supported by program CAPES/PNPD grant number 1271113.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycles ; Non-smooth differential systems ; Piecewise linear differential system
Published in:	Journal of mathematical analysis and applications, Vol. 445 (2017) , p. 631-649, ISSN 1096-0813

DOI: 10.1016/j.jmaa.2016.07.022

Postprint 30 p, 478.1 KB

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