Results overview: Found 36 records in 0.02 seconds.
Articles, 36 records found
Articles 36 records found  1 - 10nextend  jump to record:
1.
On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory / Acosta Humánez, Primitivo B. (Universidad del Atlántico and Intelectual.Co. Department of Mathematics (Colombia)) ; Tomás Lázaro, José (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I) ; Morales Ruiz, Juan J. (Universidad Politécnica de Madrid. Departamento de Matemática Aplicada) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I)
We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results for some families of quadratic vector fields, Liénard equations and equations related with special functions such as Hypergeometric and Heun ones. [...]
2015 - 10.3934/dcds.2015.35.1767
Discrete and Continuous Dynamical Systems- Series A, Vol. 35, Issue 5 (May 2015) , p. 1767-1800  
2.
15 p, 434.9 KB New Family of Centers of Planar Polynomial Differential Systems of Arbitrary Even Degree / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mousavi, Marzieh (Isfahan University of Technology. Department of Mathematical Sciences) ; Nabavi, Arefeh (Isfahan University of Technology. Department of Mathematical Sciences)
The problem of distinguishing between a focus and a center is one of the classical problems in the qualitative theory of planar differential systems. In this paper, we provide a new family of centers of polynomial differential systems of arbitrary even degree. [...]
2019 - 10.1007/s10883-019-09432-x
Journal of Dynamical and Control Systems, Vol. 25, issue 4 (Oct. 2019) , p. 619-630  
3.
21 p, 408.3 KB Zero entropy for some birational maps of C² / Cimà, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zafar, Sundus (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this study, we consider a special case of the family of birational maps f:C² → C² , which were dynamically classified by [13]. We identify the zero entropy subfamilies of f and explicitly give the associated invariant fibrations. [...]
2019 - 10.1016/j.jmaa.2018.11.047
Journal of mathematical analysis and applications, Vol. 474, Issue 2 (June 2019) , p. 765-781  
4.
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  
5.
12 p, 275.2 KB On Darboux integrability of Edelstein's reaction system in R³ / Ferragut, Antoni (Universitat Jaume I. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemàtica) ; Wiuf, Carsten (Københavns Universitet. Department of Mathematical Sciences)
We consider Edelstein's dynamical system of three reversible reactions in R³ and show that it is not Darboux integrable. To do so we characterize its polynomial first integrals, Darboux polynomials and exponential factors.
2018 - 10.1016/j.chaos.2018.01.029
Chaos, solitons and fractals, Vol. 108 (March 2018) , p. 129-135  
6.
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  
7.
22 p, 505.3 KB Dynamics, integrability and topology for Lotka-Volterra Hamiltonian systems in R^4 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Xiao, Dongmei (Shanghai Jiao Tong University. School of Mathematical Sciences)
In this paper first we give the sufficient and necessary conditions in order that two classes of polynomial Kolmogorov systems in \R_ ^4 are Hamiltonian systems. After we study the integrability of these Hamiltonian systems in the Liouville sense. [...]
2017 - 10.1016/j.jde.2016.10.042
Journal of differential equations, Vol. 262 Núm. 3 (2017) , p. 2231-2253  
8.
13 p, 696.9 KB Periodic orbits of continuous and discontinuous piecewise linear differential systems via first integrals / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Teixeira, Marco Antonio (Universidade Estadual de Campinas (Brasil). Departamento de Matemática)
2017 - 10.1007/s40863-017-0064-x
São Paulo Journal of Mathematical Sciences, 2017  
9.
11 p, 721.3 KB On the polynomial integrability of a system motivated by the Riemann ellipsoid problem / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We consider differential systems obtained by coupling two Euler-Poinsot systems. The motivation to consider such systems can be traced back to the Riemann ellipsoid problem. We provide new cases for which these systems are completely integrable. [...]
2016
ESAIM. Control, Optimisation and Calculus of Variations, Vol. 22 (2016) , p. 872-882  
10.
17 p, 401.0 KB Global phase portraits of quadratic systems with an ellipse and a straight line as invariant algebraic curves / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Yu, Jiang (Shanghai Jiao Tong University. Department of Mathematics)
In this article we study a class of integrable quadratic systems and classify all its phase portraits. More precisely, we characterize the class of all quadratic polynomial differential systems in the plane having an ellipse and a straight line as invariant algebraic curves. [...]
2015
Electronic journal of differential equations, Vol. 314 (2015) , p. 1-14  

Articles : 36 records found   1 - 10nextend  jump to record:
Interested in being notified about new results for this query?
Set up a personal email alert or subscribe to the RSS feed.