Lower Bounds on the Number of Limit Cycles for a Class of Hamiltonian Systems
We study the weak Hilbert problem for the Hamiltonian family [Formula: see text] [Formula: see text] under arbitrary polynomial perturbations of degree [Formula: see text], where [Formula: see text]. Using the first-order averaging method in generalized polar coordinates, we prove that the maximum number of limit cycles that can bifurcate from the periodic orbits of the unperturbed center is at least [Formula: see text].
Authors
- Jaume Llibre (ORCID: https://orcid.org/0000-0002-9511-5999)
- Bruno Rodrigues de Freitas (ORCID: https://orcid.org/0000-0002-8799-4313)
- Gerardo H. Anacona (ORCID: https://orcid.org/0009-0002-3721-1840)
Institutions
- Universitat Autònoma de Barcelona (ES)
- Fundação de Apoio a Pesquisa do Estado de Goiás (BR)
- Universidade Federal de Goiás (BR)
Publication Details
- Journal
- International Journal of Bifurcation and Chaos
- Published
- 2026-10-13
- DOI
- https://doi.org/10.1142/s0218127427500295
- Primary Topic
- Advanced Differential Equations and Dynamical Systems
- Type
- article
- Field-Weighted Citation Impact
- 0.00