A new result on averaging theory for a class of discontinuous planar differential systems with applications
Itikawa, Jackson (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Novaes, Douglas D. (Universidade Estadual de Campinas. Departamento de Matemática (Brazil))

Date:	2017
Abstract:	We develop the averaging theory at any order for computing the periodic solutions of periodic discontinuous piecewise differential system of the form dr/dθ= r'={F+(θ, r, ϵ) if 0≤ θ ≤ α, F-(θ, r, ϵ) if α ≤ θ ≤ 2π, where F±(θ, r, ϵ) = Σk i=1 ϵiF± i (θ, r) + ϵk+1R ± (θ, r, ϵ) with θ ϵ S and r ϵ D, where D is an open interval of ℝ+, and ϵ is a small real parameter. Applying this theory, we provide lower bounds for the maximum number of limit cycles that bifurcate from the origin of quartic polynomial differential systems of the form x = -y+xp(x, y), y = x+yp(x, y), with p(x, y) a polynomial of degree 3 without constant term, when they are perturbed, either inside the class of all continuous quartic polynomial differential systems, or inside the class of all discontinuous piecewise quartic polynomial differential systems with two zones separated by the straight line y = 0.
Grants:	Ministerio de Economía y Competitividad MTM2009-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999
Note:	Altres ajuts: ICREA Academia
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Periodic solution ; Averaging method ; Non-smooth diferential system ; Discontinuous diferential system ; Uniform isochronous center
Published in:	Revista Matemática Iberoamericana, Vol. 33, Issue 4 (2017) , p. 1247-1265, ISSN 0213-2230

DOI: 10.4171/rmi/970

Postprint 17 p, 362.7 KB

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