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Articles, 33 registres trobats
Articles 33 registres trobats  1 - 10següentfinal  anar al registre:
1.
16 p, 686.2 KB Generalized analytic integrability of a class of polynomial differential systems in C2 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tian, Yuzhou (Sun Yat-sen University. School of Mathematics (China).)
This paper study the type of integrability of differential systems with separable variables x˙=h(x)f(y), y˙ = g(y), where h, f and g are polynomials. We provide a criterion for the existence of generalized analytic first integrals of such differential systems. [...]
2021 - 10.1007/s10440-021-00407-4
Acta Applicandae Mathematicae, Vol. 173, Issue 1 (June 2021) , art. 1  
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2.
17 p, 655.4 KB 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  
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3.
12 p, 664.4 KB Formal Weierstrass nonintegrability criterion for some classes of polynomial differential systems in C² / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper, we present a criterion for determining the formal Weierstrass nonintegrability of some polynomial differential systems in the plane C². The criterion uses solutions of the form y = f(x) of the differential system in the plane and their associated cofactors, where f(x) is a formal power series. [...]
2020 - 10.1142/S0218127420500649
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 30, Issue 4 (March 2020) , art. 2050064  
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4.
25 p, 748.9 KB On the integrability of a tritrophic food chain model / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Instituto Superior Técnico. Departamento de Matemática (Portugal))
In this paper we work with a vastly analyzed tritrophic food chain model. We provide a complete characterization of their Darboux polynomials and of their exponential factors. We also show the non-existence of polynomial first integrals, of rational first integrals, of local analytic first integrals in a neighborhood of the origin, of first integrals that can be described by formal series and of Darboux first integrals.
2010 - 10.1515/ans-2010-0206
Advanced Nonlinear Studies, Vol. 10, Issue 2 (May 2010) , p. 331-355  
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5.
12 p, 271.2 KB On the integrability of the Hamiltonian systems with homogeneus polynomial potentials / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiao Tong University. School of Mathematical Sciences (China))
We summarize the known results on the integrability of the complex Hamiltonian systems with two degrees of freedom defined by the Hamiltonian functions of the form H = 1/2 2 ∑ i=1 p2i + V (q1,q2), where V (q1,q2) are homogeneous polynomial potentials of degree k.
2018 - 10.2478/AMNS.2018.2.00041
Applied Mathematics and Nonlinear Sciences, Vol. 3, Issue 2 (July 2018) , p. 527-536
2 documents
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6.
15 p, 767.1 KB On the mechanisms for producing linear type centers in polynomial differential systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we study the different mechanisms that give rise to linear type centers for polynomial differential systems. The known mechanisms are the algebraic reversibility and the Liouville integrability. [...]
2018
Moscow Mathematical Journal, Vol. 18, Issue 3 (July-September 2018) , p. 409-420  
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7.
19 p, 716.5 KB Strongly formal weierstrass non-integrability for polynomial differential systems in C2 / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Recently a criterion has been given for determining the weakly formal Weierstrass non-integrability of polynomial differential systems in C2. Here we extend this criterion for determining the strongly formal Weierstrass non-integrability which includes the weakly formal Weierstrass non-integrability of polynomial differential systems in C2. [...]
2020 - 10.14232/ejqtde.2020.1.1
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 2020, Issue 1 (2020) , p. 1-16
2 documents
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8.
10 p, 661.5 KB On the integrability of Hamiltonian systems with d degrees of freedom and homogenous polynomial potential of degree n / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
We consider Hamiltonian systems with d degrees of freedom and a Hamiltonian of the form H = 1/2 d∑i=1 p21+V(q1,. . . ,qd), where V is a homogenous polynomial of degree n ≥ 3. We prove that such Hamiltonian systems with n odd or n = 4m, have a Darboux first integral if and only if they have a polynomial first integral.
2018 - 10.1142/S0219199717500456
Communications in Contemporary Mathematics, Vol. 20, Issue 8 (December 2018) , art. 1750045  
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9.
13 p, 678.3 KB On the Darboux integrability of the logarithmic galactic potentials / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
We study the logarithmic Hamiltonians H=(p +p )∕2+log(1+x+y∕q), which appear in the study of the galactic dynamics. We characterize all the invariant algebraic hypersurfaces and all exponential factors of the Hamiltonian system with Hamiltonian H. [...]
2017 - 10.1016/j.geomphys.2017.07.019
Journal of geometry and physics, Vol. 121 (November 2017) , p. 279-287  
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10.
13 p, 731.7 KB On the Darboux integrability of the Hindmarsh-Rose burster / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We study the Hindmarsh–Rose burster which can be described by the differential system x?=y?x3+bx2+I?z,y?=1?5x2?y,z?=?(s(x?x0)?z), where b, I, ?, s, x0 are parameters. We characterize all its invariant algebraic surfaces and all its exponential factors for all values of the parameters. [...]
2018 - 10.1007/s10114-017-5661-1
Acta Mathematica Sinica. English Series, Vol. 34, issue 6 (2018) , p. 947-958  
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Articles : 33 registres trobats   1 - 10següentfinal  anar al registre:
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