Birth of limit cycles for a classe of continuous and discontinuous differential systems in (d 2)-dimension
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Teixeira, Marco Antonio (Universidade Estadual de Campinas(Brazil). Departamento de Matemática)
Zeli, Iris O. (Universidade Estadual de Campinas(Brazil). Departamento de Matemática)

Data:	2016
Resum:	The orbits of the reversible differential system ˙x = −y, ˙y = x, ˙z = 0, with x, y ∈ R and z ∈ R d, are periodic with the exception of the equilibrium points (0, 0, z1, . . . , zd). We compute the maximum number of limit cycles which bifurcate from the periodic orbits of the system ˙x = −y, ˙y = x, ˙z = 0, using the averaging theory of first order, when this system is perturbed, first inside the class of all polynomial differential systems of degree n, and second inside the class of all discontinuous piecewise polynomial differential systems of degree n with two pieces, one in y > 0 and the other in y < 0. In the first case this maximum number is nd(n − 1)/2, and in the second is nd(n − 1).
Ajuts:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 318999 European Commission 316338
Nota:	Agraïments: FEDER/UNAB10-4E-378. The second author is partially supported by a FAPESP-BRAZIL grant 2012/18780-0. The third author is partially supported by a FAPESP-BRAZIL grant 2012/23591-1 and 2013/21078-8.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Averaging theory ; Discontinuous polynomial differential system ; Limit cycle ; Periodic orbit
Publicat a:	Dynamical Systems, Vol. 31 Núm. 3 (2016) , p. 237-250, ISSN 1468-9375

DOI: 10.1080/14689367.2015.1102868

Postprint 16 p, 737.1 KB

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