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UAB Digital Repository of Documents 10 records found  Search took 0.02 seconds. 
1.
10 p, 652.9 KB Limit cycles for a class of third-order differential equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Yu, Jiang (Shanghai Jiaotong University. Department of Mathematics (China)) ; Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics (China))
In this paper we study the limit cycles of the third-order differential equation . . . x − μẍ + ẋ − μx = εF(x, ẋ , ẍ, t) where μ ≠ 0, ε is small enough and F Є C2 is a 2π-periodic function of variable t.
2010 - 10.1216/RMJ-2010-40-2-581
The Rocky Mountain Journal of Mathematics, Vol. 40, Issue 2 (2010) , p. 581-594
2 documents
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2.
10 p, 607.1 KB Integrability of reversible and equivariant quadratic polynomial differential systems in the plane / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
We study the existence of first integrals for the class of reversible and equivariant quadratic polynomial differential systems in the plane. We put special emphasis in the study of the analytic first integrals.
2019 - 10.1216/RMJ-2019-49-2-579
The Rocky Mountain Journal of Mathematics, Vol. 49, Issue 2 (2019) , p. 579-591  
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3.
8 p, 319.1 KB Invariant curves and integrability of planar Cr differential systems / Ferragut Amengual, Antoni Manel (Universitat Jaume I. Institut Universitari de Matemàtiques i Aplicacions de Castelló) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We improve the known expressions of the Cr differential systems in the plane having a given Cr+1 invariant curve, or a given Cr+1 first integral. Their application to polynomial differential systems having either an invariant algebraic curve, or a first integral, also improves the known results on such systems.
2018 - 10.1216/RMJ-2018-48-5-1537
The Rocky Mountain Journal of Mathematics, Vol. 48, Issue 5 (2018) , p. 1537-1550  
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4.
18 p, 669.2 KB Polynomial first integrals for weight-homogeneous planar polynomial differential systems of weight degree 4 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Instituto Superior Técnico. Departamento de Matemática (Portugal))
We classify all of the weight-homogeneous planar polynomial differential systems of weight degree 4 having a polynomial first integral.
2016 - 10.1216/RMJ-2016-46-5-1619
The Rocky Mountain Journal of Mathematics, Vol. 46, Issue 5 (2016) , p. 1619-1642  
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5.
21 p, 834.1 KB Centers for generalized quintic polynominal differential systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matematica)
2017 - 10.1216/RMJ-2017-47-4-1097
The Rocky Mountain Journal of Mathematics, Vol. 47 Núm. 4 (2017) , p. 1097-1120  
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6.
6 p, 1.8 MB Periods of continuous maps on closed surfaces / Guirao, Juan Luis Garcia (Universidad Politécnica de Cartagena. Departamento de Matemática Aplicada y Estadística) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
2017 - 10.1216/RMJ-2017-47-4-1089
The Rocky Mountain Journal of Mathematics, Vol. 47 Núm. 4 (2017) , p. 1089-1096  
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7.
13 p, 1.9 MB Liouvillian first integrals for quadratic systems with an integrable saddle / Bolaños Rivera, Yudy Marcela (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We provide explicit expressions for the Liouvillian first integrals of the quadratic polynomial differential systems having an integrable saddle.
2015 - 10.1216/RMJ-2015-45-6-1765
The Rocky Mountain Journal of Mathematics, Vol. 45 Núm. 6 (2015) , p. 1765-1779  
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8.
25 p, 507.7 KB Planar real polynomial differential systems of degree n>3 having a weak focus of high order / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Rabanal, Roland (The Abdus Salam International Centre for Theoretical Physics (Italy))
We construct planar polynomial differential systems of even (respectively odd) degree n > 3, of the form linear plus a nonlinear homogeneous part of degree n having a weak focus of order n2 − 1 (respectively n2−1/2) at the origin. [...]
2012 - 10.1216/RMJ-2012-42-2-657
The Rocky Mountain Journal of Mathematics, Vol. 42 Núm. 2 (2012) , p. 657-693  
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9.
37 p, 2.3 MB Phase portraits and invariant straight lines of cubic polynomial vector fields having a quadratic rational first integral / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mahdi, Adam (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vulpe, Nicolae (Academy of Sciences of Moldova. Institute of Mathematics and Computer Science)
2011 - 10.1216/RMJ-2011-41-5-1585
The Rocky Mountain Journal of Mathematics, Vol. 41 Núm. 5 (2011) , p. 1585-1629  
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10.
53 p, 2.7 MB From topological to geometric equivalence in the classification of singularities at infinity for quadratic vector fields / Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Schlomiuk, Dana (Université de Montréal. Département de Mathématiques et de Statistiques) ; Vulpe, Nicolae (Academy of Sciences of Moldova. Institute of Mathematics and Computer Science)
In the topological classification of phase portraits no distinctions are made between a focus and a node and neither are they made between a strong and a weak focus or between foci of different orders. [...]
2015 - 10.1216/RMJ-2015-45-1-29
The Rocky Mountain Journal of Mathematics, Vol. 45 Núm. 1 (2015) , p. 29-113  
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