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Rigid centres on the center manifold of tridimensional differential systems

Part of: General theory in ordinary differential equations Qualitative theory

Published online by Cambridge University Press:  07 September 2021

Adam Mahdi ,
Claudio Pessoa Open the ORCID record for Claudio Pessoa [Opens in a new window]  and
Jarne D. Ribeiro Open the ORCID record for Jarne D. Ribeiro [Opens in a new window]
Adam Mahdi
Affiliation:
Department of Engineering Science, Institute of Biomedical Engineering, University of Oxford, Oxford, UK (adam.mahdi@eng.ox.ac.uk) Faculty of Applied Mathematics, AGH University of Science and Technology, Krakw, Poland
Claudio Pessoa
Affiliation:
Departamento de Matemática, Universidade Estadual Paulista, IBILCE/UNESP, Rua Cristovão Colombo, 2265, 15.054-000, São José do Rio Preto, SP, Brazil (c.pessoa@unesp.br)
Jarne D. Ribeiro
Affiliation:
Instituto Federal de Educação, Ciência e Tecnologia do Sul de Minas Gerais, IFSULDEMINAS, Rua Mario Ribola 409, Penha II, 37903-358, Passos, MG, Brazil (jarne.ribeiro@ifsuldeminas.edu.br)
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Abstract

Motivated by the definition of rigid centres for planar differential systems, we introduce the study of rigid centres on the center manifolds of differential systems on $\mathbb {R}^{3}$. On the plane, these centres have been extensively studied and several interesting results have been obtained. We present results that characterize the rigid systems on $\mathbb {R}^{3}$ and solve the centre-focus problem for several families of rigid systems.

Keywords

Centre-focus problemcenter manifoldfirst integralrigid centre

MSC classification

Primary: 34C05: Location of integral curves, singular points, limit cycles
Secondary: 34A34: Nonlinear equations and systems, general
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 4 , August 2022 , pp. 1058 - 1080
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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