Hamiltonian system with 2 degrees of freedom - Resultats de la cerca

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Resultats globals: 4 registres trobats en 0.04 segons.
Articles, 4 registres trobats

Articles	4 registres trobats

11 p, 404.9 KB

Meromorphic integrability of the Hamiltonian systems with homogeneous potentials of degree -4 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tian, Yuzhou (Sun Yat-sen University. School of Mathematics (China))
We characterize the meromorphic Liouville integrability of the Hamiltonian systems with Hamiltonian H=(p21+p22)/2+1/P(q1,q2), being P(q1,q2) a homogeneous polynomial of degree 4 of one of the following forms ±q41, 4q31q2, ±6q21q22, ±(q21+q22)2, ±q22(6q21−q22), ±q22(6q21+q22), q41+6μq21q22−q42, −q41+6μq21q22+q42 with μ>−1/3 and μ≠1/3, and q41+6μq21q22+q42 with μ≠±1/3. [...]
2021 - DOI (Digital Object Identifier)

10.3934/dcdsb.2021228
Discrete and continuous dynamical systems. Series B, 2021

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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 - DOI (Digital Object Identifier)

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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15 p, 852.9 KB

Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree -3 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mahdi, Adam (University of North Carolina at Charlotte. Mathematics Department) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
In this paper we study the polynomial integrability of natural Hamiltonian systems with two degrees of freedom having a homogeneous potential of degree k given either by a polynomial, or by an inverse of a polynomial. [...]
2011 - DOI (Digital Object Identifier)

10.1016/j.physd.2011.09.003
Physica D. Nonlinear phenomena, Vol. 240 (2011) , p. 1928-1935

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9 p, 770.9 KB

Analytic integrability of Hamiltonian systems with exceptional potentials / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We study the existence of analytic first integrals of the complex Hamiltonian systems of the form H = 1 2 ∑ 2 i=1 p 2 i + Vl(q1, q2) with the homogeneous polynomial potential Vl(q1, q2) = α(q2 − iq1) L (q2 + iq1) k−l , l = 0, . [...]
2015 - DOI (Digital Object Identifier)

10.1016/j.physleta.2015.07.034
Physics Letters. A, Vol. 379 (2015) , p. 2295-2299

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