scholarly journals Non-nested configuration of algebraic limit cycles in quadratic systems

2006 ◽  
Vol 225 (2) ◽  
pp. 513-527 ◽  
Author(s):  
J. Chavarriga ◽  
I.A. García ◽  
J. Sorolla
Keyword(s):  
Limit Cycles ◽  
Quadratic Systems ◽  
Algebraic Limit Cycles ◽  
Algebraic Limit

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.

scholarly journals Uniqueness of Algebraic Limit Cycles for Quadratic Systems

2001 ◽  
Vol 261 (1) ◽  
pp. 85-99 ◽  
Author(s):  
Javier Chavarriga ◽  
Hector Giacomini ◽  
Jaume Llibre
Keyword(s):  
Limit Cycles ◽  
Quadratic Systems ◽  
Algebraic Limit Cycles ◽  
Algebraic Limit

scholarly journals Algebraic limit cycles of degree 4 for quadratic systems

2004 ◽  
Vol 200 (2) ◽  
pp. 206-244 ◽  
Author(s):  
Javier Chavarriga ◽  
Jaume Llibre ◽  
Jordi Sorolla
Keyword(s):  
Limit Cycles ◽  
Quadratic Systems ◽  
Algebraic Limit Cycles ◽  
Algebraic Limit

scholarly journals The Cubic Polynomial Differential Systems with two Circles as Algebraic Limit Cycles

2018 ◽  
Vol 18 (1) ◽  
pp. 183-193 ◽  
Author(s):  
Jaume Giné ◽  
Jaume Llibre ◽  
Claudia Valls
Keyword(s):  
Limit Cycles ◽  
Differential Systems ◽  
Polynomial Differential Systems ◽  
Cubic Polynomial ◽  
Algebraic Limit Cycles ◽  
Algebraic Limit

AbstractIn this paper we characterize all cubic polynomial differential systems in the plane having two circles as invariant algebraic limit cycles.

scholarly journals On the 16th Hilbert problem for algebraic limit cycles

2010 ◽  
Vol 248 (6) ◽  
pp. 1401-1409 ◽  
Author(s):  
Jaume Llibre ◽  
Rafael Ramírez ◽  
Natalia Sadovskaia
Keyword(s):  
Limit Cycles ◽  
Hilbert Problem ◽  
16Th Hilbert Problem ◽  
Algebraic Limit Cycles ◽  
Algebraic Limit
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