Weak Hilbert problem - Search Results - UAB Digital Repository of Documents

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Articles, 6 records found

Articles	6 records found

5 p, 726.8 KB

Limit cycles for a variant of a generalized Riccati equation / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemàtica)
In this paper we provide a lower bound for the maximum number of limit cycles surrounding the origin of systems (x, y = x) given by a variant of the generalized Riccati equation \[ x x^2n 1 x b x^4n 3=0, \] where b>0, b \R, n is a non--negative integer and is a small parameter. [...]
2017 - DOI (Digital Object Identifier)

10.1016/j.aml.2016.11.016
Applied mathematics letters, Vol. 68 (2017) , p. 76-79

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25 p, 401.8 KB

Limit cycles coming from some uniform isochronous centers / Liang, Haihua (Guangdong Polytechnic Normal University(China). Department of Computer Science) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
This article is about the weak 16--th Hilbert problem, i. e. we analyze how many limit cycles can bifurcate from the periodic orbits of a given polynomial differential center when it is perturbed inside a class of polynomial differential systems. [...]
2016 - DOI (Digital Object Identifier)

10.1515/ans-2015-5010
Advanced Nonlinear Studies, Vol. 16 Núm. 2 (2016) , p. 197-220

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15 p, 386.1 KB

Upper bounds for the number of zeroes for some Abelian integrals / Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Consider the vector field x' = −yG(x, y), y' = xG(x, y), where the set of critical points {G(x, y) = 0} is formed by K straight lines, not passing through the origin and parallel to one or two orthogonal directions. [...]
2012 - DOI (Digital Object Identifier)

10.1016/j.na.2012.04.033
Nonlinear Analysis : Theory, Methods and Applications, Vol. 75 (2012) , p. 5169-5179

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11 p, 279.4 KB

Limit cycles appearing from the perturbation of a system with a multiple line of critical points / Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Consider the planar ordinary differential equation ˙x = −y(1 − y)m, y˙ = x(1 − y)m, where m is a positive integer number. We study the maximum number of zeroes of the Abelian integral M that controls the limit cycles that bifurcate from the period annulus of the origin when we perturb it with an arbitrary polynomial vector field. [...]
2012 - DOI (Digital Object Identifier)

10.1016/j.na.2011.08.032
Nonlinear Analysis : Theory, Methods and Applications, Vol. 75 (2012) , p. 278-285

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12 p, 350.1 KB

Complete Abelian integrals for polynomials whose generic fiber is biholomorphic to C^* / Rebollo-Perdomo, Salomón (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Let H be a polynomial of degree m + 1 on C2 such that its generic fiber is biholomorphic to C∗, and let ω be an arbitrary polynomial 1-form of degree n on C2. We give an upper bound depending only on m and n for the number of isolated zeros of the complete Abelian integral defined by H and ω.
2012 - DOI (Digital Object Identifier)

10.1016/j.jmaa.2012.05.014

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12 p, 390.4 KB

Bifurcation of limit cycles from some uniform isochronous centers / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makhlouf, Ammar (University of Annaba. Department of Mathematics)
This article concerns with the weak 16-th Hilbert problem. More precisely, we consider the uniform isochronous centers x'=-y x^(n-1) y, y'= x x^(n-2) y^2 , for n = 2, 3, 4, and we perturb them by all homogeneous polynomial of degree 2, 3, 4, respectively. [...]
2015
Dynamics of Continuous, Discrete and Impulsive Systems. Series A. Mathematical Analysis, Vol. 22, Num. 5 (2015) , p. 381-394

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