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rigid centre

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Rigid centres on the center manifold of tridimensional differential systems
Part of
- Qualitative theory
- General theory in ordinary differential equations
Adam Mahdi, Claudio Pessoa, Jarne D. Ribeiro
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 152 / Issue 4 / August 2022

Published online by Cambridge University Press:

07 September 2021, pp. 1058-1080

Print publication:

August 2022
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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.