Limit cycles of linear vectors on manifolds

Jaume Llibre; Xiang Zhang

Limit cycles of linear vectors on manifolds

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

Resumen

It is well known that linear vector fields on the manifold R^n cannot have limit cycles, but this is not the case for linear vector fields on other manifolds. We study the periodic orbits of linear vector fields on different manifolds, and motivate and present an open problem on the number of limit cycles of linear vector fields on a class of C^1 connected manifold.

Idioma original	Inglés
Páginas (desde-hasta)	3120-3131
Número de páginas	12
Publicación	Nonlinearity
Volumen	29
Estado	Aceptada en prensa - 2016

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https://ddd.uab.cat/record/169478

Algunos aspectos de la dinamica global de los sistemas diferenciales: integrabilidad, soluciones periodicas y bifurcaciones
Llibre Salo, J. (Principal Investigator), Torregrosa i Arús, J. (Investigador/a Principal 2), Geyer , A. (Colaborador/a), Pérez González, S. (Colaborador/a), Artes Ferragud, J. C. (Investigador/a), Caubergh , M. M. (Investigador/a), Cima Mollet, A. M. (Investigador/a), Corbera Subirana, M. (Investigador/a), Cors Iglesias, J. M. (Investigador/a), Ferragut, A. (Investigador/a), Gasull Embid, A. (Investigador/a), Pantazi, C. (Investigador/a), Schlomiuk, D. (Investigador/a), Valls, C. (Investigador/a) & Vulpe, N. (Investigador/a)
Ministerio de Economía y Competitividad (MINECO)
1/01/14 → 31/12/17
Proyecto: Proyectos y Ayudas de Investigación

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title = "Limit cycles of linear vectors on manifolds",

abstract = "It is well known that linear vector fields on the manifold R^n cannot have limit cycles, but this is not the case for linear vector fields on other manifolds. We study the periodic orbits of linear vector fields on different manifolds, and motivate and present an open problem on the number of limit cycles of linear vector fields on a class of C^1 connected manifold.",

keywords = "Averaging method, Center, Isochronous center, Limit cycle, Periodic orbit",

author = "Jaume Llibre and Xiang Zhang",

year = "2016",

language = "English",

volume = "29",

pages = "3120--3131",

journal = "Nonlinearity",

issn = "0951-7715",

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TY - JOUR

T1 - Limit cycles of linear vectors on manifolds

AU - Llibre, Jaume

AU - Zhang, Xiang

PY - 2016

Y1 - 2016

N2 - It is well known that linear vector fields on the manifold R^n cannot have limit cycles, but this is not the case for linear vector fields on other manifolds. We study the periodic orbits of linear vector fields on different manifolds, and motivate and present an open problem on the number of limit cycles of linear vector fields on a class of C^1 connected manifold.

AB - It is well known that linear vector fields on the manifold R^n cannot have limit cycles, but this is not the case for linear vector fields on other manifolds. We study the periodic orbits of linear vector fields on different manifolds, and motivate and present an open problem on the number of limit cycles of linear vector fields on a class of C^1 connected manifold.

KW - Averaging method

KW - Center

KW - Isochronous center

KW - Limit cycle

KW - Periodic orbit

M3 - Article

SN - 0951-7715

VL - 29

SP - 3120

EP - 3131

JO - Nonlinearity

JF - Nonlinearity

ER -

Limit cycles of linear vectors on manifolds

Resumen

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Proyectos

Algunos aspectos de la dinamica global de los sistemas diferenciales: integrabilidad, soluciones periodicas y bifurcaciones

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