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Articles, 13 records found
Articles 13 records found  1 - 10next  jump to record:
1.
18 p, 698.2 KB The center problem for the class of Λ- Ω differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Ramírez, Valentín (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The center problem, i. e. distinguish between a focus and a center, is a classical problem in the qualitative theory of planar differential equations which go back to Darboux, Poincaré and Liapunov. [...]
2020 - 10.1007/s12215-020-00568-5
Rendiconti del Circolo Matematico di Palermo, vol. 70 (October 2020) p. 1483-1499  
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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.
47 p, 952.2 KB An inverse approach to the center problem / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Ramírez, Valentín (Universitat de Barcelona)
We consider analytic or polynomial vector fields of the form X=(-y+X)∂∂x+(x+Y)∂∂y, where X= X(x, y)) and Y= Y(x, y)) start at least with terms of second order. It is well-known that X has a center at the origin if and only if X has a Liapunov-Poincaré local analytic first integral of the form H=12(x2+y2)+∑j=3∞Hj, where H = H (x, y) is a homogenous polynomial of degree j. [...]
2019 - 10.1007/s12215-018-0342-1
Rendiconti del Circolo Matematico di Palermo, Vol. 68, Issue 1 (April 2019) , p. 29-64  
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4.
37 p, 871.8 KB An inverse approach to the center-focus problem for polynomial differential system with homogenous nonlinearities / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Ramírez, Valentín (Universitat de Barcelona)
We consider polynomial vector fields of the form \[ \X=(-y X_m) x (x Y_m) y, \] where X_m=X_m(x,y) and Y_m=Y_m(x,y) are homogenous polynomials of degree m. It is well--known that \X has a center at the origin if and only if \X has an analytic first integral of the form \[ H=12(x^2 y^2) _j=3^ H_j, \] where H_j=H_j(x,y) is a homogenous polynomial of degree j. [...]
2017 - 10.1016/j.jde.2017.04.030
Journal of differential equations, Vol. 263 (2017) , p. 3327-3369  
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5.
5 p, 607.4 KB On the analytic integrability of the 5-dimensional Lorenz system for the gravitiy-wave activity / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Saghin, Radu (Universitat Autònoma de Barcelona. Centre de Recerca per a l'Educació Científica i Matemàtica) ; Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics)
The 5-dimensional Lorenz system for the coupled Rosby and gravity waves has exactly two independent analytic first integrals.
2014 - 10.1090/S0002-9939-2013-11773-9
Proceedings of the American Mathematical Society, Vol. 142 Núm. 2 (2014) , p. 531-537  
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6.
14 p, 337.6 KB Local Darboux first integrals of analytic differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Walcher, Sebastian (RWTH Aachen(Germany). Lehrstuhl A fur Mathematik) ; Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics)
In this paper we discuss local and formal Darboux first integrals of analytic differential systems, using the theory of Poincaré Dulac normal forms. We study the effect of local Darboux integrability on analytic normalization. [...]
2014 - 10.1016/j.bulsci.2013.09.007
Bulletin des Sciences Mathematiques, Vol. 138 (2014) , p. 71-88  
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7.
19 p, 649.4 KB Integrability of the Rucklidge system / Lima, Mauricio Firmino Silva (Universidade Federal do ABC(Brazil). Centro de Matemática Computacâo e Cognicâo) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We study the Darboux and the analytic integrability of the Rucklidge system.
2014 - 10.1007/s11071-014-1389-y
Nonlinear Dynamics, Vol. 77 (2014) , p. 1441-1453  
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8.
18 p, 403.1 KB Analytic integrability of the Bianchi Class A cosmological models with 0 k < 1 / Ferragut Amengual, Antoni Manel (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I)
There are many works studying the integrability of the Bianchi class A cosmologies with k = 1. Here we characterize the analytic integrability of the Bianchi class A cosmological models when 0 ≤ k < 1.
2013 - 10.1016/j.chaos.2012.12.007
Chaos, solitons and fractals, Vol. 48 (2013) , p. 12-21  
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9.
11 p, 580.6 KB Local analytic first integrals of planar analytic differential systems / Colak, Ilker (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 study the existence of local analytic first integrals of a class of analytic differential systems in the plane, obtained from the Chua's system studied in [6, 7, 11]. The method used can be applied to other analytic differential systems.
2013 - 10.1016/j.physleta.2013.03.001
Physics Letters. A, Vol. 377 Núm. 15 (2013) , p. 1065-1069  
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10.
18 p, 424.3 KB Local behavior of planar analytic vector fields via integrability / Álvarez Torres, María Jesús (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica) ; Ferragut Amengual, Antoni Manel (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I)
We present an algorithm to study the local behavior of singular points of planar analytic vector fields having a first integral which is a quotient of analytic functions. The algorithm is based on the blow up method. [...]
2012 - 10.1016/j.jmaa.2011.06.062
Journal of mathematical analysis and applications, Vol. 385 (2012) , p. 264-277  
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