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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.)

Limit cycles of piecewise polynomial perturbations of higher dimensional linear differential systems

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Author(s):
Llibre, Jaume [1] ; Novaes, Douglas D. [2] ; Zeli, Iris O. [3]
Total Authors: 3
Affiliation:
[1] Univ Autonoma Barcelona UAB, Dept Matemat, Barcelona 08193, Catalonia - Spain
[2] Univ Estadual Campinas, Dept Matemat, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil
[3] Inst Tecnol Aeronaut ITA, Dept Matemat, Praca Marechal Eduardo Gomes 50, BR-12228900 Sao Jose Dos Campos, SP - Brazil
Total Affiliations: 3
Document type: Journal article
Source: REVISTA MATEMATICA IBEROAMERICANA; v. 36, n. 1, p. 291-318, 2020.
Web of Science Citations: 1
Abstract

The averaging theory has been extensively employed for studying periodic solutions of smooth and nonsmooth differential systems. Here, we extend the averaging theory for studying periodic solutions a class of regularly perturbed non-autonomous n-dimensional discontinuous piecewise smooth differential system. As a fundamental hypothesis, it is assumed that the unperturbed system has a manifold Z subset of R-n of periodic solutions satisfying dim(Z) < n. Then, we apply this result to study limit cycles bifurcating from periodic solutions of linear differential systems, x' = Mx, when they are perturbed inside a class of discontinuous piecewise polynomial differential systems with two zones. More precisely, we study the periodic solutions of the following differential system: x' = Mx + epsilon F-1(n)(x) + epsilon F-2(2)n(x) in Rd+2, where e is a small parameter, M is a (d+2) x(d+2) matrix having one pair of pure imaginary conjugate eigenvalues, m zeros eigenvalues, and d - m non-zero real eigenvalues. (AU)

FAPESP's process: 18/16430-8 - Global dynamics of nonsmooth differential equations
Grantee:Douglas Duarte Novaes
Support Opportunities: Regular Research Grants
FAPESP's process: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II
Grantee:Claudio Aguinaldo Buzzi
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 18/13481-0 - Geometry of control, dynamical and stochastic systems
Grantee:Marco Antônio Teixeira
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 13/21078-8 - Periodic solutions dor discontinuous dynamical systems with symmetry
Grantee:Iris de Oliveira Zeli
Support Opportunities: Scholarships abroad - Research Internship - Post-doctor