Hamiltonian nilpotent saddles of linear plus cubic homogeneous polynomial vector fields

Nonlinear Analysis Real World Applications ◽

10.1016/j.nonrwa.2021.103451 ◽

2022 ◽

Vol 64 ◽

pp. 103451

Author(s):

Montserrat Corbera ◽

Claudia Valls

Keyword(s):

Homogeneous Polynomial ◽

Vector Fields ◽

Polynomial Vector ◽

Polynomial Vector Fields

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Centers of weight-homogeneous polynomial vector fields on the plane

Proceedings of the American Mathematical Society ◽

10.1090/proc/13393 ◽

2016 ◽

Vol 145 (6) ◽

pp. 2539-2555 ◽

Cited By ~ 2

Author(s):

Jaume Giné ◽

Jaume Llibre ◽

Claudia Valls

Keyword(s):

Homogeneous Polynomial ◽

Vector Fields ◽

Polynomial Vector ◽

Polynomial Vector Fields

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Structural Stability of Planar Homogeneous Polynomial Vector Fields: Applications to Critical Points and to Infinity

Journal of Differential Equations ◽

10.1006/jdeq.1996.0038 ◽

1996 ◽

Vol 125 (2) ◽

pp. 490-520 ◽

Cited By ~ 20

Author(s):

Jaume Llibre ◽

Jesús S. Pérez del Río ◽

José Angel Rodríguez

Keyword(s):

Structural Stability ◽

Critical Points ◽

Homogeneous Polynomial ◽

Vector Fields ◽

Polynomial Vector ◽

Polynomial Vector Fields

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On the centers of the weight-homogeneous polynomial vector fields on the plane

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2009.06.036 ◽

2009 ◽

Vol 359 (2) ◽

pp. 722-730 ◽

Cited By ~ 14

Author(s):

Jaume Llibre ◽

Claudio Pessoa

Keyword(s):

Homogeneous Polynomial ◽

Vector Fields ◽

Polynomial Vector ◽

Polynomial Vector Fields

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Algebraic classification of homogeneous polynomial vector fields in the plane

Japan Journal of Industrial and Applied Mathematics ◽

10.1007/bf03167299 ◽

1996 ◽

Vol 13 (1) ◽

pp. 63-91 ◽

Cited By ~ 8

Author(s):

C. B. Collins

Keyword(s):

Homogeneous Polynomial ◽

Vector Fields ◽

Polynomial Vector ◽

Polynomial Vector Fields ◽

Algebraic Classification

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Phase portraits for quadratic homogeneous polynomial vector fields on % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqr1ngB % PrgifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaqFr0x % c9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8fr % Fve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaatuuDJX % wAK1uy0HMmaeHbfv3ySLgzG0uy0HgiuD3BaGqbaiab-jj8tnaaCaaa % leqabaGaaGOmaaaaaaa!4488! $$ \mathbb{S}^2 $$

Rendiconti del Circolo Matematico di Palermo (1952 -) ◽

10.1007/s12215-009-0030-2 ◽

2009 ◽

Vol 58 (3) ◽

pp. 361-406 ◽

Cited By ~ 5

Author(s):

Jaume Llibre ◽

Claudio Pessoa

Keyword(s):

Homogeneous Polynomial ◽

Vector Fields ◽

Phase Portraits ◽

Polynomial Vector ◽

Polynomial Vector Fields

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Limit cycles for planar semi-quasi-homogeneous polynomial vector fields

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2012.07.060 ◽

2013 ◽

Vol 397 (1) ◽

pp. 276-284 ◽

Cited By ~ 5

Author(s):

Yulin Zhao

Keyword(s):

Limit Cycles ◽

Homogeneous Polynomial ◽

Vector Fields ◽

Polynomial Vector ◽

Polynomial Vector Fields

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Number of Invariant Straight Lines for Homogeneous Polynomial Vector Fields of Arbitrary Degree and Dimension

Journal of Dynamics and Differential Equations ◽

10.1007/s10884-009-9141-x ◽

2009 ◽

Vol 21 (3) ◽

pp. 487-499 ◽

Cited By ~ 3

Author(s):

Jaume Llibre ◽

Violetta Pilyugina

Keyword(s):

Homogeneous Polynomial ◽

Vector Fields ◽

Polynomial Vector ◽

Polynomial Vector Fields ◽

Arbitrary Degree ◽

Straight Lines

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Bifurcation diagrams for Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields

Journal of Differential Equations ◽

10.1016/j.jde.2017.02.001 ◽

2017 ◽

Vol 262 (11) ◽

pp. 5518-5533 ◽

Cited By ~ 7

Author(s):

Ilker E. Colak ◽

Jaume Llibre ◽

Claudia Valls

Keyword(s):

Homogeneous Polynomial ◽

Vector Fields ◽

Polynomial Vector ◽

Bifurcation Diagrams ◽

Polynomial Vector Fields

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Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields

Journal of Differential Equations ◽

10.1016/j.jde.2014.05.024 ◽

2014 ◽

Vol 257 (5) ◽

pp. 1623-1661 ◽

Cited By ~ 14

Author(s):

Ilker E. Colak ◽

Jaume Llibre ◽

Claudia Valls

Keyword(s):

Homogeneous Polynomial ◽

Vector Fields ◽

Polynomial Vector ◽

Polynomial Vector Fields ◽

Linear Type

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Two-Dimensional Homogeneous Polynomial Vector Fields with Common Factors

Journal of Mathematical Analysis and Applications ◽

10.1006/jmaa.1994.1061 ◽

1994 ◽

Vol 181 (3) ◽

pp. 836-863 ◽

Cited By ~ 2

Author(s):

C.B. Collins

Keyword(s):

Homogeneous Polynomial ◽

Vector Fields ◽

Common Factors ◽

Two Dimensional ◽

Polynomial Vector ◽

Polynomial Vector Fields

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