Results overview: Found 157 records in 0.01 seconds.
Articles, 155 records found
Research literature, 2 records found
Articles 155 records found  1 - 10nextend  jump to record:
1.
Polynomial Hamiltonian systems of degree 3 with nilpotent saddles / Corbera Subirana, Montserrat (Universitat de Vic - Universitat Central de Catalunya. Facultat de Ciències i Tecnologia) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica (Portugal))
We provide normal forms and the global phase portraits in the Poincaré disk for all Hamiltonian planar polynomial vector fields of degree 3 symmetric with respect to the x−axis having a nilpotent saddle at the origin.
2021 - 10.3934/dcdsb.2020225
Discrete and continuous dynamical systems. Series B, Vol. 26, Issue 6 (June 2021) , p. 3209-3233  
2.
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)  
3.
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  
4.
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  
5.
Dynamics and Darboux integrability of the D 2 polynomial vector fields of degree 2 in ℝ3 / Ginoux, Jean-Marc (Centre National de la Recherche Scientifique. Université de Toulon. Centre de Physique Théorique (France)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
We characterize the Darboux integrability and the global dynamics of the 3-dimensional polynomial differential systems of degree 2 which are invariant under the D2 symmetric group, which have been partially studied previously by several authors.
2021 - 10.1007/s11040-020-09372-0
Mathematical Physics, Analysis and Geometry, Vol. 24, Issue 1 (March 2021) , art. 1  
6.
41 p, 690.3 KB The 16th Hilbert problem for discontinuous piecewise isochronous centers of degree one or two separated by a straight line / Esteban, Marina (Universidad de Sevilla. Escuela Técnica Superior de Ingeniería. Departamento de Matemática Aplicada II/Instituto de Matemáticas (IMUS)) ; 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 discontinuous piecewise differential systems formed by two differential systems separated by a straight line when these two differential systems are linear centers (which always are isochronous) or quadratic isochronous centers. [...]
2021 - 10.1063/5.0023055
Chaos, Vol. 31, Issue 4 (April 2021) , art. 043112  
7.
Configurations of the topological indices of the planar polynomial differential systems of degree (2, m) / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
Using the Euler-Jacobi formula there is a relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the polynomial differential systems x˙ = P(x, y), y˙ = Q(x, y) with degree of P equal to 2 and degree of Q equal to m when these systems have 2m finite singular points.
2021 - 10.1007/s00025-020-01322-0
Results in Mathematics, Vol. 76, Issue 1 (March 2021) , art. 21  
8.
36 p, 651.2 KB On the singularities of the planar cubic polynomial differential systems and the Euler Jacobi formula / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
Using the Euler-Jacobi formula we obtain an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the planar cubic polynomial differential systems when these systems have nine finite singular points.
2020 - 10.1007/s12346-020-00435-9
Qualitative Theory of Dynamical Systems, Vol. 19, Issue 3 (December 2020) , art. 96  
9.
Limit cycles of discontinuous piecewise differential systems formed by linear centers in R2 and separated by two circles / Anacleto, Maria Elisa (Universidad del Bio-Bio. Departamento de Matemática (Chile)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal)) ; Vidal, Claudio (Universidad del Bio-Bio. Departamento de Matemática (Chile))
We show that discontinuous planar piecewise differential systems formed by linear centers and separated by two concentric circles can have at most three limit cycles. Usually is a difficult problem to provide the exact upper bound that a class of differential systems can exhibit. [...]
2021 - 10.1016/j.nonrwa.2020.103281
Nonlinear Analysis: Real World Applications, Vol. 60 (August 2021) , art. 103281  
10.
8 p, 544.8 KB The Euler-Jacobi formula and the planar quadratic-quartic polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
The Euler-Jacobi formula provides an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the planar quadratic-quartic polynomial differential systems when these systems have eight finite singular points.
2021 - 10.1090/proc/15257
Proceedings of the American Mathematical Society, Vol. 149, Issue 1 (January 2021) , p. 135-141  

Articles : 155 records found   1 - 10nextend  jump to record:
Research literature 2 records found  
1.
129 p, 1.1 MB Hamiltonian linear type centers and nilpotent centers of linear plus cubic polynomial vector fields / Evrim Colak, Ilker ; Llibre, Jaume, dir. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia, 1973-, dir. ; Universitat Autònoma de Barcelona. Departament de Matemàtiques
En este trabajo proporcionamos doce formas normales para todos los campos vectoriales polinomiales Hamiltonianos en el plano que tienen términos lineales más cúbicos homogéneos y que poseen en el origen un centro de tipo lineal o un centro nilpotente. [...]
In this work we provide twelve normal forms for all the Hamiltonian planar polynomial vector fields having linear plus cubic homogeneous terms which possess a linear type center or a nilpotent center at the origin, and find their global phase portraits on the Poincaré disk. [...]

[Barcelona] : Universitat Autònoma de Barcelona, 2014  
2.
162 p, 983.1 KB Generalizaciones de la teoría de integrabilidad de Darboux para campos de vectores polinomiales / Bolaños Rivera, Yudy Marcela ; Llibre, Jaume, dir. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia, 1973-, dir. ; Universitat Autònoma de Barcelona. Departament de Matemàtiques
En matemáticas, la integrabilidad de los campos de vectores polinomiales ha sido objeto de estudio desde hace más de cien años. En 1878, Darboux dio unas condiciones que permiten establecer la existencia de una integral prime- ra para estos campos. [...]
In mathematics, the integrability of polynomial vector fields has been studied for more than one hundred years. In 1878, Darboux provided conditions to establish the existence of first integrals for these fields. [...]

[Barcelona] : Universitat Autònoma de Barcelona, 2013  

See also: similar author names
2 Valls, Carme
157 Valls, Claudia
157 Valls, Claudia
3 Valls, Claudia,
3 Valls, Clàudia,
Interested in being notified about new results for this query?
Set up a personal email alert or subscribe to the RSS feed.