Chiellini hamiltonian liÉnard differential systems

Jaume Giné; Jaume Llibre; Claudia Valls

Chiellini hamiltonian liÉnard differential systems

Jaume Giné, Jaume Llibre, Claudia Valls

Department of Mathematics

Research output: Contribution to journal › Article › Research

Abstract

© 2019 Texas State University. We characterize the centers of the Chiellini Hamiltonian Liénard second-order differential equations x′ = y, y′ = −f(x)y − g(x) where g(x) = f(x)(k − α(1 + α)∫ f(x)dx) with α, k ∈ R. Moreover we study the phase portraits in the Poincaré disk of these systems when f(x) is linear.

Original language	English
Article number	71
Journal	Electronic Journal of Differential Equations
Volume	2019
Publication status	Published - 1 Jan 2019

Keywords

Center-focus problem
First integrals
Liénard system

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https://ddd.uab.cat/record/222609

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title = "Chiellini hamiltonian li{\'E}nard differential systems",

abstract = "{\textcopyright} 2019 Texas State University. We characterize the centers of the Chiellini Hamiltonian Li{\'e}nard second-order differential equations x′ = y, y′ = −f(x)y − g(x) where g(x) = f(x)(k − α(1 + α)∫ f(x)dx) with α, k ∈ R. Moreover we study the phase portraits in the Poincar{\'e} disk of these systems when f(x) is linear.",

keywords = "Center-focus problem, First integrals, Li{\'e}nard system",

author = "Jaume Gin{\'e} and Jaume Llibre and Claudia Valls",

year = "2019",

month = jan,

day = "1",

language = "English",

volume = "2019",

journal = "Electronic Journal of Differential Equations",

issn = "1072-6691",

publisher = "Texas State University - San Marcos",

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TY - JOUR

T1 - Chiellini hamiltonian liÉnard differential systems

AU - Giné, Jaume

AU - Llibre, Jaume

AU - Valls, Claudia

PY - 2019/1/1

Y1 - 2019/1/1

N2 - © 2019 Texas State University. We characterize the centers of the Chiellini Hamiltonian Liénard second-order differential equations x′ = y, y′ = −f(x)y − g(x) where g(x) = f(x)(k − α(1 + α)∫ f(x)dx) with α, k ∈ R. Moreover we study the phase portraits in the Poincaré disk of these systems when f(x) is linear.

AB - © 2019 Texas State University. We characterize the centers of the Chiellini Hamiltonian Liénard second-order differential equations x′ = y, y′ = −f(x)y − g(x) where g(x) = f(x)(k − α(1 + α)∫ f(x)dx) with α, k ∈ R. Moreover we study the phase portraits in the Poincaré disk of these systems when f(x) is linear.

KW - Center-focus problem

KW - First integrals

KW - Liénard system

M3 - Article

VL - 2019

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

SN - 1072-6691

M1 - 71

ER -