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On the Global Nilpotent Centers of Cubic Polynomial Hamiltonian Systems

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Abstract

A global center for a vector field in the plane is a singular point p having \(\mathbb {R}^2\) filled of periodic orbits with the exception of the singular point p. Polynomial differential systems of degree 2 have no global centers. In this paper we classify the global nilpotent centers of planar cubic polynomial Hamiltonian systems symmetric with respect to the y-axis.

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Acknowledgements

We thank to the reviewers their comments and suggestions which helped us to improve the paper. The first and third authors are supported by FCT/Portugal through CAMGSD, IST-ID, projects UIDB/04459/2020 and UIDP/04459/2020. The second author is supported by the Agencia Estatal de Investigación grant PID2019-104658GB-I00, and the H2020-MSCA-RISE-2017-777911.

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Authors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049–001, Lisboa, Portugal

    Luis Barreira & Clàudia Valls

  2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, 08193, Barcelona, Catalonia, Spain

    Jaume Llibre

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  1. Luis Barreira
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  2. Jaume Llibre
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  3. Clàudia Valls
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Correspondence to Luis Barreira.

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Barreira, L., Llibre, J. & Valls, C. On the Global Nilpotent Centers of Cubic Polynomial Hamiltonian Systems. Differ Equ Dyn Syst (2022). https://doi.org/10.1007/s12591-022-00606-x

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