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dc.rights.licenseLicencia de Creative Commons Reconocimiento-NoComercial-CompartirIgual 4.0 Internacionalspa
dc.contributor.authorAcosta-Humánez, P.
dc.contributor.authorAlvarez-Ramírez, M.
dc.contributor.authorStuchi, T.J.
dc.date.accessioned2018-02-08T14:59:21Z
dc.date.available2018-02-08T14:59:21Z
dc.date.issued2018-01-09
dc.identifier.issn15360040
dc.identifier.urihttp://hdl.handle.net/20.500.12442/1725
dc.description.abstractWe show the nonintegrability of the three-parameter Armburster--Guckenheimer--Kim quartic Hamiltonian using Morales--Ramis theory, with the exception of the three already known integrable cases. We use Poincaré sections to illustrate the breakdown of regular motion for some parameter values.spa
dc.language.isoengspa
dc.publisherSociedad de Matemática Industrial y Aplicadaspa
dc.sourceVol. 17, No.1 (2018)eng
dc.sourceRevista SIAMspa
dc.source.urihttps://doi.org/10.1137/16M1080689
dc.subjectHamiltonianeng
dc.subjectIntegrability of dynamical systemseng
dc.subjectDiferential Galois theoryeng
dc.subjectLegendre equationeng
dc.subjectSchrodinger equationeng
dc.titleNonintegrability of the Armbruster-Guckenheimer-Kim Quartic Hamiltonian Through Morales-Ramis Theoryeng
dc.typearticlespa
dcterms.referencesR. Abraham and J. E. Marsden, Foundations of Mechanics, Benjamin Cummings, San Francisco, 1978.eng
dcterms.referencesM. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables, Wiley, New York, 1984.eng
dcterms.referencesP. Acosta-Hum anez and D. Bl azquez-Sanz, Non-integrability of some Hamiltonians with rational potential, Discrete Contin. Dyn. Syst. Ser. B, 10 (2008), pp. 265{293, https://doi.org/10.3934/dcdsb. 2008.10.265.eng
dcterms.referencesP. B. Acosta-Hum anez, Galoisian Approach to Supersymmetric Quantum Mechanics. The Integrability Analysis of the Schr odinger Equation by Means of Di erential Galois Theory, VDM Verlag Dr. M uller, Berlin, 2010.eng
dcterms.referencesP. B. Acosta-Hum anez, J. L azaro, J. Morales-Ruiz, and C. Pantazi, On the integrability of polynomial vector elds in the plane by means of Picard-Vessiot theory, Discrete Contin. Dyn. Syst., 35 (2015), pp. 1767{1800, https://doi.org/10.3934/dcds.2015.35.1767.eng
dcterms.referencesP. B. Acosta-Hum anez, J. Morales-Ruiz, and J. A. Weil, Galoisian approach to integrability of Schr odinger equation, Rep. Math. Phys., 67 (2011), pp. 305{374, https://doi.org/10.1016/ S0034-4877(11)60019-0.eng
dcterms.referencesP. Andrle, A third integral of motion in a system with a potential of the fourth degree, Phys. Lett. A, 17 (1966), pp. 169{175.eng
dcterms.referencesD. Armbruster, J. Guckenheimer, and S. Kim, Chaotic dynamics in systems with square symmetry, Phys. Lett. A, 140 (1989), pp. 416{420, https://doi.org/10.1016/0375-9601(89)90078-9.eng
dcterms.referencesA. Bostan, T. Combot, and M. E. Din, Computing necessary integrability conditions for planar parametrized homogeneous potentials, in Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, 2014, pp. 67{74, https://doi.org/10.1145/2608628.2608662.eng
dcterms.referencesG. Contopoulos, Galactic Dynamics, Princeton University Press, Princeton, NJ, 1988.eng
dcterms.referencesA. A. Elmandouh, On the dynamics of Armbruster-Guckenheimer-Kim galactic potential in a rotating reference frame, Astrophys. Space Sci., 361 (2016), pp. 182{194, https://doi.org/10.1007/ s10509-016-2770-8.eng
dcterms.referencesJ. Hietarinta, Direct methods for the search of the second invariant, Phys. Rep., 147 (1987), pp. 87{154.eng
dcterms.referencesI. Kaplansky, An Introduction to Di erential Algebra, Hermann, Paris, 1957.eng
dcterms.referencesE. Kolchin, Di erential Algebra and Algebraic Groups, Pure and Appl. Math. 59, Academic Press, New York, 1973.eng
dcterms.referencesJ. Llibre and L. Roberto, Periodic orbits and non-integrability of Armbruster-Guckenheimer-Kim potential, Astrophys. Space Sci., 343 (2013), pp. 69{74, https://doi.org/10.1007/s10509-012-1210-7.eng
dcterms.referencesA. Maciejewski and M. Przybylska, Darboux points and integrability of Hamiltonian systems with homogeneous polynomial potential, J. Math. Phys., 46 (2005), 062901, https://doi.org/10.1063/1. 1917311.eng
dcterms.referencesJ. Morales-Ruiz, Di erential Galois Theory and Non-Integrability of Hamiltonian Systems, Progr. Math. 178, Birkhauser, Basel, 1999.eng
dcterms.referencesJ. Morales-Ruiz and J. P. Ramis, Integrability of dynamical systems through di erential galois theory: A practical guide, in Di erential Algebra, Complex Analysis and Orthogonal Polynomials, Contemp. Math. 509, AMS, Providence, RI, 2010, pp. 143{220, http://dx.doi.org/10.1090/conm/509.eng
dcterms.referencesJ. J. Morales-Ruiz and J. P. Ramis, Galoisian obstructions to integrability of Hamiltonian systems I, Methods Appl. Anal., 8 (2001), pp. 33{96, https://doi.org/10.4310/MAA.2001.v8.n1.a3.eng
dcterms.referencesJ. J. Morales-Ruiz and J. P. Ramis, Galoisian obstructions to integrability of Hamiltonian systems II, Methods Appl. Anal., 8 (2001), pp. 97{112, https://doi.org/10.4310/MAA.2001.v8.n1.a4.eng
dcterms.referencesK. Nakagawa, Direct Construction of Polynomial First Integrals for Hamiltonian Systems with a Two- Dimensional Homogeneous Polynomial Potential, Ph.D. thesis, Department of Astronomical Science, Graduate University for Advanced Study and the National Astronomical Observatory of Japan, 2002.eng
dcterms.referencesG. P oschl and E. Teller, Bemerkungen zur quantenmechanik des anharmonischen oszillators, Z. Phys., 83 (1933), pp. 143{151.eng
dcterms.referencesF. Simonelli and J. P. Gollub, Surface wave mode interactions: E ects of symmetry and degeneracy, J. Fluid Mech., 199 (1989), pp. 471{494, https://dx.doi.org/10.1017/S0022112089000443.eng
dcterms.referencesE. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Di erential Equations, Part I, 2nd ed., Oxford University Press, Oxford, UK, 1962.eng
dcterms.referencesM. van der Put and M. Singer, Galois Theory of Linear Di erential Equations, Grundlehren Math. Wiss. 328, Springer, Berlin, 2003.eng
dcterms.referencesS. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer, New York, 1990.eng
dcterms.referencesH. Yoshida, Nonintegrability of the truncated Toda lattice Hamiltonian at any order, Comm. Math. Phys., 116 (1988), pp. 529{538.eng
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