Invariant algebraic curves and rational first integrals of holomorphic foliations in CP(2)

2003 ◽  
Vol 46 (2) ◽  
pp. 271 ◽  
Author(s):  
Xiang ZHANG
Keyword(s):  
Algebraic Curves ◽  
First Integrals ◽  
Holomorphic Foliations ◽  
Invariant Algebraic Curves

scholarly journals A note on Liouvillian first integrals and invariant algebraic curves

2013 ◽  
Vol 26 (2) ◽  
pp. 285-289 ◽  
Author(s):  
Jaume Giné ◽  
Maite Grau ◽  
Jaume Llibre
Keyword(s):  
Algebraic Curves ◽  
First Integrals ◽  
Invariant Algebraic Curves

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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