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Preface
Non-integrability criterium for normal variational equations around an integrable subsystem and an example: The Wilberforce spring-pendulum
1. | Departamento de Matemáticas y Estadística, Universidad del Norte, Barranquilla, Colombia |
2. | Departamento de Matemáticas, UAM-Iztapalapa, 09340 Iztapalapa, México, D.F., Mexico |
3. | Universidad Sergio Arboleda, Calle 74 no. 14-14, Bogotá, D.C. |
4. | Departamento de Matemáticas, Universidad Autónoma Metropolitana – Iztapalapa, 09340 Iztapalapa, México, D. F. |
References:
[1] |
P. B. Acosta-Humanez, "Galoisian Approach to Supersymmetric Quantum Mechanics. The Integrability Analysis of the Schrodinger Equation by Means of Differential Galois Theory,", VDM Verlag, (2010). Google Scholar |
[2] |
P. B. Acosta-Humanez, J. J. Morales-Ruiz and J. A. Weil, Galoisian approach to integrability of the schrödinger equation,, Rep. Math. Phys., 67 (2011), 305.
|
[3] |
R. H. Berg and T. S. Marshall, Wilberforce pendulum oscillations and normal modes,, Am. J. Phys., 59 (1991), 32.
doi: 10.1119/1.16702. |
[4] |
D. Blázquez-Sanz and J. J. Morales-Ruiz, Differential Galois theory of algebraic Lie-Vessiot systems, Differential algebra, complex analysis and orthogonal polynomials,, Contemp. Math., 509 (2010), 1.
|
[5] |
R. C. Churchill, J. Delgado and D. L. Rod, The spring pendulum system and the Riemann equation,, New trends for Hamiltonian systems and celestial mechanics, 8 (1996), 97.
|
[6] |
J. Kovacic, An algorithm for solving second order linear homogeneous differential equations,, J. Symbolic Computation, 2 (1986), 3.
doi: 10.1016/S0747-7171(86)80010-4. |
[7] |
A. Maciejewski, M. Przybylska and J. A. Weil, Non-integrability of the generalized spring-pendulum problem,, J. Phys. A, 37 (2004), 2579.
|
[8] |
R. Martínez and C. Simó, Non-integrability of the degenerate cases of the swinging Atwood's machine using higher order variational equations,, Discrete Contin. Dyn. Syst., 29 (2011), 1.
|
[9] |
J. J. Morales-Ruiz, "Differential Galois Theory and Non-integrability of Hamiltonian Systems,", Progress in Mathematics 179, (1999).
|
[10] |
J. J. Morales-Ruiz and J. P. Ramis, Galoisian obstructions to integrability of hamiltonian systems I,, Methods Appl. Anal., 8 (2001), 33.
|
[11] |
J. J. Morales-Ruiz and J. P. Ramis, Galoisian obstructions to integrability of hamiltonian systems II,, Methods Appl. Anal., 8 (2001), 97. Google Scholar |
[12] |
J. J. Morales-Ruiz, C. Simó and S. Simon, Algebraic proof of the non-integrability of Hill's problem,, Ergodic Theory Dynam. Systems, 25 (2005), 1237.
|
[13] |
J. J. Morales-Ruiz, J. P. Ramis and C. Simó, Integrability of hamiltonian systems and differential Galois groups of higher variational equations,, Ann. Sci. École Norm. Sup. (4), 40 (2007), 845.
|
[14] |
J. Muñoz, J. Rodríguez and F. J. Muriel, Weil bundles and Jet spaces,, Czech. Math. J., 50 (2000), 721.
|
[15] |
J. Martinet and J. P. Ramis, Théorie de Galois différentielle et resommation,, Computer algebra and differential equations, (1990), 117.
|
show all references
References:
[1] |
P. B. Acosta-Humanez, "Galoisian Approach to Supersymmetric Quantum Mechanics. The Integrability Analysis of the Schrodinger Equation by Means of Differential Galois Theory,", VDM Verlag, (2010). Google Scholar |
[2] |
P. B. Acosta-Humanez, J. J. Morales-Ruiz and J. A. Weil, Galoisian approach to integrability of the schrödinger equation,, Rep. Math. Phys., 67 (2011), 305.
|
[3] |
R. H. Berg and T. S. Marshall, Wilberforce pendulum oscillations and normal modes,, Am. J. Phys., 59 (1991), 32.
doi: 10.1119/1.16702. |
[4] |
D. Blázquez-Sanz and J. J. Morales-Ruiz, Differential Galois theory of algebraic Lie-Vessiot systems, Differential algebra, complex analysis and orthogonal polynomials,, Contemp. Math., 509 (2010), 1.
|
[5] |
R. C. Churchill, J. Delgado and D. L. Rod, The spring pendulum system and the Riemann equation,, New trends for Hamiltonian systems and celestial mechanics, 8 (1996), 97.
|
[6] |
J. Kovacic, An algorithm for solving second order linear homogeneous differential equations,, J. Symbolic Computation, 2 (1986), 3.
doi: 10.1016/S0747-7171(86)80010-4. |
[7] |
A. Maciejewski, M. Przybylska and J. A. Weil, Non-integrability of the generalized spring-pendulum problem,, J. Phys. A, 37 (2004), 2579.
|
[8] |
R. Martínez and C. Simó, Non-integrability of the degenerate cases of the swinging Atwood's machine using higher order variational equations,, Discrete Contin. Dyn. Syst., 29 (2011), 1.
|
[9] |
J. J. Morales-Ruiz, "Differential Galois Theory and Non-integrability of Hamiltonian Systems,", Progress in Mathematics 179, (1999).
|
[10] |
J. J. Morales-Ruiz and J. P. Ramis, Galoisian obstructions to integrability of hamiltonian systems I,, Methods Appl. Anal., 8 (2001), 33.
|
[11] |
J. J. Morales-Ruiz and J. P. Ramis, Galoisian obstructions to integrability of hamiltonian systems II,, Methods Appl. Anal., 8 (2001), 97. Google Scholar |
[12] |
J. J. Morales-Ruiz, C. Simó and S. Simon, Algebraic proof of the non-integrability of Hill's problem,, Ergodic Theory Dynam. Systems, 25 (2005), 1237.
|
[13] |
J. J. Morales-Ruiz, J. P. Ramis and C. Simó, Integrability of hamiltonian systems and differential Galois groups of higher variational equations,, Ann. Sci. École Norm. Sup. (4), 40 (2007), 845.
|
[14] |
J. Muñoz, J. Rodríguez and F. J. Muriel, Weil bundles and Jet spaces,, Czech. Math. J., 50 (2000), 721.
|
[15] |
J. Martinet and J. P. Ramis, Théorie de Galois différentielle et resommation,, Computer algebra and differential equations, (1990), 117.
|
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