On a class of cubic planar polynomial foliations

Jaume Llibre; Gerardo Rodríguez

On a class of cubic planar polynomial foliations

Jaume Llibre, Gerardo Rodríguez

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

Phase portraits of quadratic planar polynomial foliations are classified. Recently several papers deal with the phase portraits of cubic polynomial foliations. In this paper we determine all phase portraits of cubic planar polynomial foliations defined by all vector fields having the first component equal to a non-zero constant and the second one equal to an arbitrary cubic polynomial.

Original language	English
Pages (from-to)	67-97
Journal	Dynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm
Volume	4
Issue number	1
Publication status	Published - 1 Mar 1998

Cite this

@article{f7a615a0cb964bc7ad7cb75ed813456f,

title = "On a class of cubic planar polynomial foliations",

abstract = "Phase portraits of quadratic planar polynomial foliations are classified. Recently several papers deal with the phase portraits of cubic polynomial foliations. In this paper we determine all phase portraits of cubic planar polynomial foliations defined by all vector fields having the first component equal to a non-zero constant and the second one equal to an arbitrary cubic polynomial.",

author = "Jaume Llibre and Gerardo Rodr{\'i}guez",

year = "1998",

month = mar,

day = "1",

language = "English",

volume = "4",

pages = "67--97",

journal = "Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms",

issn = "1492-8760",

publisher = "Watam Press",

number = "1",

}

TY - JOUR

T1 - On a class of cubic planar polynomial foliations

AU - Llibre, Jaume

AU - Rodríguez, Gerardo

PY - 1998/3/1

Y1 - 1998/3/1

N2 - Phase portraits of quadratic planar polynomial foliations are classified. Recently several papers deal with the phase portraits of cubic polynomial foliations. In this paper we determine all phase portraits of cubic planar polynomial foliations defined by all vector fields having the first component equal to a non-zero constant and the second one equal to an arbitrary cubic polynomial.

AB - Phase portraits of quadratic planar polynomial foliations are classified. Recently several papers deal with the phase portraits of cubic polynomial foliations. In this paper we determine all phase portraits of cubic planar polynomial foliations defined by all vector fields having the first component equal to a non-zero constant and the second one equal to an arbitrary cubic polynomial.

M3 - Article

VL - 4

SP - 67

EP - 97

JO - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

JF - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

SN - 1492-8760

IS - 1

ER -

On a class of cubic planar polynomial foliations

Abstract

Fingerprint

Cite this