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three-dimensional systems

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

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Cyclicity of rigid centres on centre manifolds of three-dimensional systems
Part of
- Qualitative theory
- General theory in ordinary differential equations
Claudio Pessoa, Lucas Queiroz, Jarne D. Ribeiro
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 154 / Issue 1 / February 2024

Published online by Cambridge University Press:

09 February 2023, pp. 188-200

Print publication:

February 2024
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We work with polynomial three-dimensional rigid differential systems. Using the Lyapunov constants, we obtain lower bounds for the cyclicity of the known rigid centres on their centre manifolds. Moreover, we obtain an example of a quadratic rigid centre from which is possible to bifurcate 13 limit cycles, which is a new lower bound for three-dimensional quadratic systems.