Global dynamics of the Benoît system

Maurício Firmino Silva Lima; Jaume Llibre

doi:https://doi.org/10.1007/s10231-012-0318-2

Global dynamics of the Benoît system

Maurício Firmino Silva Lima, Jaume Llibre

Department of Mathematics

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

1 Citation (Scopus)

Abstract

In this paper, we work with a two-degree polynomial differential system in ℝ3 related with the canard phenomena. We show that this system is completely integrable, and we provide its global phase portrait in the Poincaré ball using the Poincaré-Lyapunov compactification. © 2012 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg.

Original language	English
Pages (from-to)	1103-1122
Journal	Annali di Matematica Pura ed Applicata
Volume	193
Issue number	4
DOIs	https://doi.org/10.1007/s10231-012-0318-2
Publication status	Published - 1 Jan 2014

Keywords

Benoît system
Equilibrium point
First integral
Heteroclinic orbit
Homoclinic orbit
Invariant manifolds
Poincaré compactification
Poincaré sphere

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https://doi.org/10.1007/s10231-012-0318-2

https://ddd.uab.cat/record/150715

Cite this

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title = "Global dynamics of the Beno{\^i}t system",

abstract = "In this paper, we work with a two-degree polynomial differential system in ℝ3 related with the canard phenomena. We show that this system is completely integrable, and we provide its global phase portrait in the Poincar{\'e} ball using the Poincar{\'e}-Lyapunov compactification. {\textcopyright} 2012 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg.",

keywords = "Beno{\^i}t system, Equilibrium point, First integral, Heteroclinic orbit, Homoclinic orbit, Invariant manifolds, Poincar{\'e} compactification, Poincar{\'e} sphere",

author = "Lima, {Maur{\'i}cio Firmino Silva} and Jaume Llibre",

year = "2014",

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doi = "https://doi.org/10.1007/s10231-012-0318-2",

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AU - Lima, Maurício Firmino Silva

AU - Llibre, Jaume

PY - 2014/1/1

Y1 - 2014/1/1

N2 - In this paper, we work with a two-degree polynomial differential system in ℝ3 related with the canard phenomena. We show that this system is completely integrable, and we provide its global phase portrait in the Poincaré ball using the Poincaré-Lyapunov compactification. © 2012 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg.

AB - In this paper, we work with a two-degree polynomial differential system in ℝ3 related with the canard phenomena. We show that this system is completely integrable, and we provide its global phase portrait in the Poincaré ball using the Poincaré-Lyapunov compactification. © 2012 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg.

KW - Benoît system

KW - Equilibrium point

KW - First integral

KW - Heteroclinic orbit

KW - Homoclinic orbit

KW - Invariant manifolds

KW - Poincaré compactification

KW - Poincaré sphere

U2 - https://doi.org/10.1007/s10231-012-0318-2

DO - https://doi.org/10.1007/s10231-012-0318-2

M3 - Article

VL - 193

SP - 1103

EP - 1122

IS - 4

ER -

Global dynamics of the Benoît system

Abstract

Keywords

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