On the Global Nilpotent Centers of Cubic Polynomial Hamiltonian Systems

Luis Barreira; Jaume Llibre; Clàudia Valls

doi:10.1007/s12591-022-00606-x

On the Global Nilpotent Centers of Cubic Polynomial Hamiltonian Systems

Luis Barreira, Jaume Llibre, Clàudia Valls

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Resum

A global center for a vector field in the plane is a singular point p having R² 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.

Idioma original	Anglès
Pàgines (de-a)	1001-1011
Nombre de pàgines	11
Revista	Differential Equations and Dynamical Systems
Volum	32
Número	4
DOIs	https://doi.org/10.1007/s12591-022-00606-x
Estat de la publicació	Publicada - 2024

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10.1007/s12591-022-00606-x

https://ddd.uab.cat/record/307747

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title = "On the Global Nilpotent Centers of Cubic Polynomial Hamiltonian Systems",

abstract = "A global center for a vector field in the plane is a singular point p having R2 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.",

keywords = "Center, Cubic polynomial differential system, Global center, Hamiltonian system, Symmetry with respect to the y-axis",

author = "Luis Barreira and Jaume Llibre and Cl{\`a}udia Valls",

note = "Funding Information: 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 Investigaci{\'o}n grant PID2019-104658GB-I00, and the H2020-MSCA-RISE-2017-777911. Publisher Copyright: {\textcopyright} 2022, Foundation for Scientific Research and Technological Innovation.",

year = "2024",

doi = "10.1007/s12591-022-00606-x",

language = "English",

volume = "32",

pages = "1001--1011",

journal = "Differential Equations and Dynamical Systems",

issn = "0971-3514",

publisher = "Springer International Publishing AG",

number = "4",

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TY - JOUR

T1 - On the Global Nilpotent Centers of Cubic Polynomial Hamiltonian Systems

AU - Barreira, Luis

AU - Llibre, Jaume

AU - Valls, Clàudia

N1 - Funding Information: 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. Publisher Copyright: © 2022, Foundation for Scientific Research and Technological Innovation.

PY - 2024

Y1 - 2024

N2 - A global center for a vector field in the plane is a singular point p having R2 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.

AB - A global center for a vector field in the plane is a singular point p having R2 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.

KW - Center

KW - Cubic polynomial differential system

KW - Global center

KW - Hamiltonian system

KW - Symmetry with respect to the y-axis

UR - https://www.scopus.com/pages/publications/85132194896

U2 - 10.1007/s12591-022-00606-x

DO - 10.1007/s12591-022-00606-x

M3 - Article

AN - SCOPUS:85132194896

SN - 0971-3514

VL - 32

SP - 1001

EP - 1011

JO - Differential Equations and Dynamical Systems

JF - Differential Equations and Dynamical Systems

IS - 4

ER -

On the Global Nilpotent Centers of Cubic Polynomial Hamiltonian Systems

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