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Pàgina inicial > Articles > Articles publicats > Limit cycles of discontinuous piecewise polynomial vector fields |
Data: | 2017 |
Resum: | When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x= -y((x^2 y^2)/2)^m and y= x((x^2 y^2)/2)^m with m 1, when we perturb it inside a class of discontinuous piecewise polynomial vector fields of degree n with k pieces. The positive integers m, n and k are arbitrary. The main tool used for proving our results is the averaging theory for discontinuous piecewise vector fields. |
Ajuts: | Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999 Ministerio de Economía y Competitividad MTM2013-40998-P |
Nota: | Agraïments: The first author is partially supported by a FAPESP/Brazil grant number 2014/02134-7, a CNPq-Brazil grant number 443302/2014-6 and CAPES grants 88881.030454/2013-01 (from the program CSF-PVE) and 1576689 (from the program PNPD). The second author is partially supported by the CAPES grant 88881.030454/2013-01 from the program CSF-PVE. D.J. Tonon is supported by grant #2012/10 26 7000 803, Goiás Research Foundation (FAPEG), PROCAD/CAPES grant 88881.068462/2014-01 and by CNPq-Brazil. |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Averaging theory ; Limit cycles ; Piecewise smooth vector fields |
Publicat a: | Journal of mathematical analysis and applications, Vol. 449 Núm. 1 (2017) , p. 572-579, ISSN 1096-0813 |
Postprint 10 p, 320.4 KB |