GSD (Grup de Sistemes Dinàmics)

Els sistemes dinàmics són, i sempre han estat, una de les principals línies d'investigació en Matemàtiques. És interès de totes les civilitzacions humanes comprendre qüestions importants, com el moviment dels planetes, l'evolució de les poblacions, o l'estudi de la dinàmica en sistemes deterministes, de manera que els sistemes dinàmics s'han convertit en un objectiu important d'estudi. Després de molts anys d'evolució, l'àrea dels sistemes dinàmics ha sofert diverses transformacions i ha desenvolupat diverses branques que han permès respondre preguntes de diversa índole.

Les linies principals d'investigació del Grup de Sistemes Dinàmics de la UAB (GSD-UAB) són: Mecànica celeste, Dinàmica complexa, Sistemes Dinàmics discrets i Teoria qualitativa d'equacions diferencials.

Els membres del nostre grup treballen principalment a les universitats catalanes (UAB, UB, UdG, UPC, URV, UVic), tot i que alguns dels nostres investigadors treballen en altres universitats d'Espanya i a l'estranger. El GSD-UAB col·labora asiduament amb diversos grups de recerca nacionals i internacionals.

Pàgina web: http://www.gsd.uab.cat

Estadístiques d'ús Els més consultats
Darreres entrades:
2021-04-29
15:31
Phase portraits of uniform isochronous centers with homogeneous nonlinearities / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
We classify the phase portraits in the Poincaré disc of the differential equations of the form x' = − y + xf(x, y), ẏ = x + yf(x, y) where f(x,y) is a homogeneous polynomial of degree n − 1 when n = 2, 3, 4, 5, and f has only simple zeroes. [...]
2021 - 10.1007/s10883-021-09529-2
Journal of Dynamical and Control Systems, (February 2021)  
2021-04-29
15:13
Dynamics of a two prey and one predator system with indirect effect / Colucci, Renato (Università Politecnica delle Marche. Dipartimento di Ingegneria Industriale e Scienze Matematiche (Italy)) ; Diz-Pita, Érika (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización) ; Otero-Espinar, M. Victoria (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización)
We study a population model with two preys and one predator, considering a Holling type II functional response for the interaction between first prey and predator and taking into account indirect effect of predation. [...]
2021 - 10.3390/math9040436
Mathematics, Vol. 9, Issue 4 (February 2021) , art. 436  
2021-04-29
13:48
A sufficient condition for the real Jacobian conjecture in R2 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
Let F = (f,g): R2 → R2 be a polynomial map such that detDF (x,y) is different from zero for all (x,y) ∈ R2. We provide some new sufficient conditions for the injectivity of F. The proofs are based on the qualitative theory of differential equations.
2021 - 10.1016/j.nonrwa.2021.103298
Nonlinear Analysis: Real World Applications, Vol. 60 (August 2021) , p. 103298  
2021-04-29
13:48
A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, X. (Shanghai Jiao Tong University. School of Mathematical Sciences and MOE-LSC (People's Republic of China))
In the qualitative theory of differential equations in the plane one of the most difficult objects to study is the existence of limit cycles. There are many papers dedicated to this subject. Here we will present a survey mainly dedicated to the algebraic and explicit non-algebraic limit cycles of the polynomial differential systems in R and of the discontinuous piecewise differential systems in R formed by two linear differential systems separated by a straight line. [...]
2021 - 10.1016/j.exmath.2020.03.001
Expositiones Mathematicae, Vol. 39, Issue 1 (March 2021) , p. 48-61  
2021-04-29
13:48
The cyclicity of the period annulus of a reversible quadratic system / Liu, Changjian (Sun Yat-sen University. School of Mathematics (China)) ; Li, Chengzhi (Peking University. School of Mathematical Sciences (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We prove that perturbing the periodic annulus of the reversible quadratic polynomial differential system x˙ = y + ax2, y˙ = −x with a ≠ 0 inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycle, including their multiplicities. [...]
2021 - 10.1017/prm.2021.2
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, (February 2021)  
2021-04-29
13:48
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, (October 2020)  
2021-04-29
13:48
Polynomial vector fields on the Clifford torus / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Murza, Adrian C. (University of Texas at Dallas. Department of Mathematical Sciences (USA))
First, we characterize all the polynomial vector fields in R4 which have the Clifford torus as an invariant surface. Then we study the number of invariant meridians and parallels that such polynomial vector fields can have on the Clifford torus as a function of the degree of these vector fields.
2021 - 10.1142/S0218127421500577
International Journal of Bifurcation and Chaos, Vol. 31, Issue 4 (March 2021) , art. 2150057  
2021-04-29
13:48
Rational limit cycles of Abel equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
In this paper we deal with Abel equations dy/dx = A(x)y2 + B(x)y3, where A(x) and B(x) are real polynomials. We prove that these Abel equations can have at most three rational limit cycles and we characterize when this happens. [...]
2021 - 10.3934/CPAA.2021007
Communications on pure & applied analysis, Vol. 20, Issue 3 (March 2021) , p. 1077-1089  
2021-04-29
13:48
Limit cycles for some families of smooth and non-smooth planar systems / Buzzi, Claudio A. (Universidade Estadual Paulista Julio de Mesquita Filho. Mathematics Department (Brazil)) ; Carvalho, Yagor Romano (Universidade Estadual Paulista Julio de Mesquita Filho. Mathematics Department (Brazil)) ; Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We apply the averaging method in a class of planar systems given by a linear center perturbed by a sum of continuous homogeneous vector fields, to study lower bounds for their number of limit cycles. [...]
2021 - 10.1016/j.na.2021.112298
Nonlinear Analysis : Theory, Methods and Applications, Vol. 207 (June 2021) , p. 112298  
2021-04-29
13:48
On the separatrix graph of a rational vector field on the Riemann sphere / Dias, Kealey (Bronx Community College of the City University of New York (USA)) ; Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
We consider the rational flow ξR(z) = R(z)(d/dz) where R is given by the quotient of two polynomials without common factors on the Riemann sphere. The separatrix graph ΓR is the boundary between trajectories with different properties. [...]
2021 - 10.1016/j.jde.2021.02.021
Journal of differential equations, Vol. 282 (May 2021) , p. 541-565