UAB Digital Repository of Documents 9 records found  Search took 0.01 seconds. 
1.
Invariant conditions for phase portraits of quadratic systems with complex conjugate invariant lines meeting at a finite point / Artés, 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 (France)) ; Vulpe, Nicolae (Vladimir Andrunakievichi Institute of Mathematics and Computer Science (Moldova))
The goal of this article is to give invariant necessary and sufficient conditions for a quadratic system, presented in whatever normal form, to have anyone of 17 out of the 20 phase portraits of the family of quadratic systems with two complex conjugate invariant lines intersecting at a finite real point. [...]
2020 - 10.1007/s12215-020-00541-2
Rendiconti del Circolo Matematico di Palermo, (July 2020)  
2.
Darboux integrability and dynamics of the Basener-Ross population model / Güngör, Faruk (Istanbul Technical University. Department of Mathematics (Turkey)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I)
We deal with the Basener and Ross model for the evolution of human population in Easter island. We study the Darboux integrability of this model and characterize all its global dynamics in the Poincaré disc, obtaining 15 different topological phase portraits.
2020 - 10.1007/s12215-020-00507-4
Rendiconti del Circolo Matematico di Palermo, (April 2020)  
3.
22 p, 510.1 KB Quadratic systems with a rational first integral of degree three : A complete classification in the coefficient space ℝ12 / Artés, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vulpe, Nicolae (Academy of Science of Moldova. Institute of Mathematics and Computer Science (Moldova))
A quadratic polynomial differential system can be identified with a single point of ℝ12 through its coefficients. The phase portrait of the quadratic systems having a rational first integral of degree 3 have been studied using normal forms. [...]
2010 - 10.1007/s12215-010-0032-0
Rendiconti del Circolo Matematico di Palermo, Vol. 59, Issue 3 (December 2010) , p. 419-449  
4.
On a conjecture on the integrability of Liénard systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Murza, Adrian C. (Insitutul de Matematică Simion Stoilow al Academiei Române) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
We consider the Liénard differential systems ̇x=y+F(x), ̇y=x (1), in C2 where F(x) is an analytic function satisfying F(0) = 0 and F'(0) ≠ 0. Then these systems have a strong saddle at the origin of coordinates. [...]
2020 - 10.1007/s12215-018-00398-6
Rendiconti del Circolo Matematico di Palermo, Vol. 69, Issue 1 (April 2020) , p. 209-216  
5.
15 p, 297.8 KB Quadratic three-dimensional differential systems having invariant planes with total multiplicity nine / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Messias, Marcelo (Universidade Estadual Paulista. Departamento de Matemática e Computação (Brazil)) ; Reinol, Alisson C. (Universidade Estadual Paulista. Instituto de Biociências, Letras e Ciências Exatas. Departamento de Matemática (Brazil))
In this paper we consider all the quadratic polynomial differential systems in R having exactly nine invariant planes taking into account their multiplicities. This is the maximum number of invariant planes that these kind of systems can have, without taking into account the infinite plane. [...]
2018 - 10.1007/s12215-018-0338-x
Rendiconti del Circolo Matematico di Palermo, Vol. 67, Issue 3 (December 2018) , p. 569-580  
6.
Linear type global centers of linear systems with cubic homogeneous nonlinearities / García Saldaña, Johanna Denise. (Universidad Católica de la Santísima Concepción. Departamento de Matemática y Física Aplicadas (Chile)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
A center p of a differential system in R2 is global if R2\ { p} is filled of periodic orbits. It is known that a polynomial differential system of degree 2 has no global centers. Here we characterize the global centers of the differential systems x˙=ax+by+P3(x,y),y˙=cx+dy+Q3(x,y),with P3 and Q3 homogeneous polynomials of degree 3, and such that the center has purely imaginary eigenvalues, i. [...]
2019 - 10.1007/s12215-019-00433-0
Rendiconti del Circolo Matematico di Palermo, (July 2019)  
7.
Global dynamics of a virus model with invariant algebraic surfaces / Dias, Fabio Scalco (Universidade Federal de Itajubá. Instituto de Matemática e Computação (Brazil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
In this paper by using the Poincaré compactification in R3 we make a global analysis for the virus system x˙=λ-dx-βxz,y˙=-ay+βxz z˙=ky-μz with (x, y, z) ∈ R3, β> 0, λ, a, d, k and μ are nonnegative parameters due to their biological meaning. [...]
2019 - 10.1007/s12215-019-00417-0
Rendiconti del Circolo Matematico di Palermo, (May 2019)  
8.
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  
9.
34 p, 480.3 KB Newton-Okounkov bodies sprouting on the valuative tree / Ciliberto, Ciro (Università di Roma. Dipartimento di Matematica) ; Farnik, Michal (Jagiellonian University (Polònia). Faculty of Mathematics and Computer Science) ; Küronya, Alex (Goethe-Universität Frankfurt am Main. Institut für Mathematik) ; Lozovanu, Victor (Université de Caen Normandie. Laboratoire de Mathématiques) ; Roé i Vellvé, Joaquim (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Shramov, Constantin
Given a smooth projective algebraic surface X, a point O∈X and a big divisor D on X, we consider the set of all Newton-Okounkov bodies of D with respect to valuations of the field of rational functions of X centred at O, or, equivalently, with respect to a flag (E, p) which is infinitely nearO, in the sense that there is a sequence of blowups X'→X, mapping the smooth, irreducible rational curve E⊂X' to O. [...]
2016 - 10.1007/s12215-016-0285-3
Rendiconti del Circolo Matematico di Palermo, 2016  

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