Global centers of a family of cubic systems

Raul Felipe Appis; Jaume Llibre

doi:10.1007/s00010-024-01051-7

Global centers of a family of cubic systems

Raul Felipe Appis, Jaume Llibre

Producción científica: Contribución a una revista › Artículo › Investigación › revisión exhaustiva

Resumen

Consider the family of polynomial differential systems of degree 3, or simply cubic systems (Formula presented.) in the plane R. An equilibrium point (x,y) of a planar differential system is a center if there is a neighborhood U of (x,y) such that U\{(x,y)} is filled with periodic orbits. When R\{(x,y)} is filled with periodic orbits, then the center is a global center. For this family of cubic systems Lloyd and Pearson characterized in Lloyd and Pearson (Comput Math Appl 60:2797-2805, 2010) when the origin of coordinates is a center. We classify which of these centers are global centers.

Idioma original	Inglés
Páginas (desde-hasta)	1373-1389
Número de páginas	17
Publicación	Aequationes Mathematicae
Volumen	98
N.º	5
DOI	https://doi.org/10.1007/s00010-024-01051-7
Estado	Publicada - oct 2024

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10.1007/s00010-024-01051-7

https://ddd.uab.cat/record/292038

Teoria qualitativa dels sistemes dinàmics amb èmfasi en les òrbites periòdiques
Llibre Salo, J. (Principal Investigator), Chas ., M. (Becario/a), Juher Barrot, D. (Becario/a), Villadelprat Yague, J. (Colaborador/a), Alseda Soler, L. (Investigador/a), Artes Ferragud, J. C. (Investigador/a), Bernat Pane, J. (Investigador/a), Casasayas Mas, J. (Investigador/a), Chavarriga Soriano, J. (Investigador/a), Cima Mollet, A. M. (Investigador/a), Corbera Subirana, M. (Investigador/a), Cors Iglesias, J. M. (Investigador/a), Falcó Montesinos, A. (Investigador/a), Gasull Embid, A. (Investigador/a), Guillamón Grabolosa, A. (Investigador/a), Jarque Ribera, X. (Investigador/a), Leseduarte Milan, M. C. (Investigador/a), Mañosa Fernández, V. (Investigador/a), Mañosas Capellades, F. (Investigador/a), Mumbrú Rodríguez, P. (Investigador/a), Soler Villanueva, J. (Investigador/a), Teruel Aguilar, A. E. (Investigador/a) & Torregrosa i Arús, J. (Investigador/a)
Dirección General de Enseñanza Superior e Investigación Científica (DGESIC)
1/12/97 → 1/12/02
Proyecto: Proyectos y Ayudas de Investigación

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title = "Global centers of a family of cubic systems",

abstract = "Consider the family of polynomial differential systems of degree 3, or simply cubic systems x ' = y , y ' = - x + a 1 x 2 + a 2 x y + a 3 y 2 + a 4 x 3 + a 5 x 2 y + a 6 x y 2 + a 7 y 3 , in the plane R 2 . An equilibrium point ( x 0 , y 0 ) of a planar differential system is a center if there is a neighborhood U of ( x 0 , y 0 ) such that U \ { ( x 0 , y 0 ) } is filled with periodic orbits. When R 2 \ { ( x 0 , y 0 ) } is filled with periodic orbits, then the center is a global center. For this family of cubic systems Lloyd and Pearson characterized in Lloyd and Pearson (Comput Math Appl 60:2797-2805, 2010) when the origin of coordinates is a center. We classify which of these centers are global centers. ",

keywords = "14R15, 37C37, Center, Cubic system, Global center, Primary 34A34, Secondary 34C25",

author = "Appis, {Raul Felipe} and Jaume Llibre",

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year = "2024",

month = oct,

doi = "10.1007/s00010-024-01051-7",

language = "English",

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journal = "Aequationes Mathematicae",

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T1 - Global centers of a family of cubic systems

AU - Appis, Raul Felipe

AU - Llibre, Jaume

N1 - © The Author(s) 2024.

PY - 2024/10

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N2 - Consider the family of polynomial differential systems of degree 3, or simply cubic systems x ' = y , y ' = - x + a 1 x 2 + a 2 x y + a 3 y 2 + a 4 x 3 + a 5 x 2 y + a 6 x y 2 + a 7 y 3 , in the plane R 2 . An equilibrium point ( x 0 , y 0 ) of a planar differential system is a center if there is a neighborhood U of ( x 0 , y 0 ) such that U \ { ( x 0 , y 0 ) } is filled with periodic orbits. When R 2 \ { ( x 0 , y 0 ) } is filled with periodic orbits, then the center is a global center. For this family of cubic systems Lloyd and Pearson characterized in Lloyd and Pearson (Comput Math Appl 60:2797-2805, 2010) when the origin of coordinates is a center. We classify which of these centers are global centers.

AB - Consider the family of polynomial differential systems of degree 3, or simply cubic systems x ' = y , y ' = - x + a 1 x 2 + a 2 x y + a 3 y 2 + a 4 x 3 + a 5 x 2 y + a 6 x y 2 + a 7 y 3 , in the plane R 2 . An equilibrium point ( x 0 , y 0 ) of a planar differential system is a center if there is a neighborhood U of ( x 0 , y 0 ) such that U \ { ( x 0 , y 0 ) } is filled with periodic orbits. When R 2 \ { ( x 0 , y 0 ) } is filled with periodic orbits, then the center is a global center. For this family of cubic systems Lloyd and Pearson characterized in Lloyd and Pearson (Comput Math Appl 60:2797-2805, 2010) when the origin of coordinates is a center. We classify which of these centers are global centers.

KW - 14R15

KW - 37C37

KW - Center

KW - Cubic system

KW - Global center

KW - Primary 34A34

KW - Secondary 34C25

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DO - 10.1007/s00010-024-01051-7

M3 - Article

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SP - 1373

EP - 1389

JO - Aequationes Mathematicae

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Global centers of a family of cubic systems

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Teoria qualitativa dels sistemes dinàmics amb èmfasi en les òrbites periòdiques

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