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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

A new result on averaging theory for a class of discontinuous planar differential systems with applications

Full text
Author(s):
Itikawa, Jackson [1] ; Llibre, Jaume [2] ; Novaes, Douglas D. [3]
Total Authors: 3
Affiliation:
[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Ave Trabalhador Sao Carlense 400, BR-13566590 Sao Carlos, SP - Brazil
[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia - Spain
[3] Univ Estadual Campinas, Dept Matemat, Rua Sergio Buarque Holanda 651, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 3
Document type: Journal article
Source: REVISTA MATEMATICA IBEROAMERICANA; v. 33, n. 4, p. 1247-1265, 2017.
Web of Science Citations: 4
Abstract

We develop the averaging theory at any order for computing the periodic solutions of periodic discontinuous piecewise differential system of the form dr/d theta = r' = [ F+(theta, r, epsilon) if 0 <= theta <= alpha, F-(theta, r, epsilon) if alpha <= theta <= 2 pi, where F-+/-(theta, r, epsilon) = Sigma(k)(i=1) epsilon(i) F-i(+/-) (theta, r) + epsilon(k+1) R-+/-(theta, r, epsilon) with theta is an element of S-1 and r is an element of D, where D is an open interval of R+, and epsilon 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)over dot> = -y + xp(x, y), <(y)over dot> = 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. (AU)

FAPESP's process: 15/02517-6 - Study of minimal sets in nonsmooth dynamical systems
Grantee:Douglas Duarte Novaes
Support Opportunities: Scholarships in Brazil - Post-Doctoral
FAPESP's process: 15/07612-7 - Uniform isochronous centers in planar polynomial differential systems of degree 5
Grantee:Jackson Itikawa
Support Opportunities: Scholarships in Brazil - Post-Doctoral
FAPESP's process: 15/24841-0 - Persistence of periodic solutions for higher order perturbed differential systems via Lyapunov-Schmidt reduction
Grantee:Douglas Duarte Novaes
Support Opportunities: Scholarships abroad - Research Internship - Post-doctor