Invariant algebraic curves linear in one variable for planar real quadratic systems

2003 ◽  
Vol 138 (2-3) ◽  
pp. 291-308 ◽  
Author(s):  
Javier Chavarriga ◽  
Maite Grau
Keyword(s):  
Algebraic Curves ◽  
Quadratic Systems ◽  
Invariant Algebraic Curves ◽  
Real Quadratic

Classification of Invariant Algebraic Curves and Nonexistence of Algebraic Limit Cycles in Quadratic Systems from Family (I) of the Chinese Classification

2020 ◽  
Vol 30 (04) ◽  
pp. 2050056 ◽  
Author(s):  
Maria V. Demina ◽  
Claudia Valls
Keyword(s):  
Differential System ◽  
Limit Cycles ◽  
Algebraic Curves ◽  
Complete Classification ◽  
Quadratic Systems ◽  
Correct Proof ◽  
Invariant Algebraic Curves ◽  
Algebraic Limit Cycles ◽  
Algebraic Limit

We give the complete classification of irreducible invariant algebraic curves in quadratic systems from family [Formula: see text] of the Chinese classification, that is, of differential system [Formula: see text] with [Formula: see text]. In addition, we provide a complete and correct proof of the nonexistence of algebraic limit cycles for these equations.

Foliations on $$\mathbb {CP}^2$$ with a unique singular point without invariant algebraic curves

2019 ◽  
Vol 207 (1) ◽  
pp. 193-200
Author(s):  
Claudia R. Alcántara ◽  
Rubí Pantaleón-Mondragón
Keyword(s):  
Singular Point ◽  
Algebraic Curves ◽  
Invariant Algebraic Curves

Explicit travelling waves and invariant algebraic curves

Nonlinearity ◽  
2015 ◽  
Vol 28 (6) ◽  
pp. 1597-1606 ◽  
Author(s):  
Armengol Gasull ◽  
Hector Giacomini
Keyword(s):  
Algebraic Curves ◽  
Travelling Waves ◽  
Invariant Algebraic Curves

On the Poincaré problem and Liouvillian integrability of quadratic Liénard differential equations

2020 ◽  
Vol 150 (6) ◽  
pp. 3231-3251 ◽  
Author(s):  
Maria V. Demina ◽  
Claudia Valls
Keyword(s):  
Differential Equations ◽  
Algebraic Curves ◽  
First Integral ◽  
Complete Classification ◽  
Invariant Algebraic Curves ◽  
Liouvillian Integrability ◽  
Poincaré Problem

AbstractWe present the complete classification of irreducible invariant algebraic curves of quadratic Liénard differential equations. We prove that these equations have irreducible invariant algebraic curves of unbounded degrees, in contrast with what is wrongly claimed in the literature. In addition, we classify all the quadratic Liénard differential equations that admit a Liouvillian first integral.

scholarly journals Invariant algebraic curves for the cubic Liénard system with linear damping

2006 ◽  
Vol 130 (5) ◽  
pp. 428-441 ◽  
Author(s):  
J. Chavarriga ◽  
I.A. García ◽  
J. Llibre ◽  
H. Żołądek
Keyword(s):  
Algebraic Curves ◽  
Liénard System ◽  
Invariant Algebraic Curves ◽  
Lienard System ◽  
Linear Damping
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