Integrability of hamiltonian systems and differential Galois groups of higher variational equations

Morales-Ruiz, Juan J.; Ramis, Jean-Pierre; Simó, Carles

doi:10.1016/j.ansens.2007.09.002

Morales-Ruiz, Juan J. ; Ramis, Jean-Pierre ; Simó, Carles

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 6, pp. 845-884.

MR Zbl | 3 citations dans Numdam

DOI : 10.1016/j.ansens.2007.09.002

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     title = {Integrability of hamiltonian systems and differential {Galois} groups of higher variational equations},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {845--884},
     publisher = {Elsevier},
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Morales-Ruiz, Juan J.; Ramis, Jean-Pierre; Simó, Carles. Integrability of hamiltonian systems and differential Galois groups of higher variational equations. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 6, pp. 845-884. doi : 10.1016/j.ansens.2007.09.002. https://www.numdam.org/articles/10.1016/j.ansens.2007.09.002/

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Ribón, Javier Finite dimensional groups of local diffeomorphisms, Israel Journal of Mathematics, Volume 227 (2018) no. 1, p. 289 | DOI:10.1007/s11856-018-1729-6
Remy, Pascal Multi-resurgence and connection-to-Stokes formulæ for some linear meromorphic differential systems, Journal of Differential Equations, Volume 264 (2018) no. 1, p. 197 | DOI:10.1016/j.jde.2017.09.004
Acosta-Humánez, Primitivo B.; Lázaro, J. Tomás; Morales-Ruiz, Juan J.; Pantazi, Chara Differential Galois theory and non-integrability of planar polynomial vector fields, Journal of Differential Equations, Volume 264 (2018) no. 12, p. 7183 | DOI:10.1016/j.jde.2018.02.016
Orieux, M.; Caillau, J.-B.; Combot, T.; Féjoz, J. Non-integrability of the minimum-time Kepler problem, Journal of Geometry and Physics, Volume 132 (2018), p. 452 | DOI:10.1016/j.geomphys.2018.06.012
Nunez, Carlos; Roychowdhury, Dibakar; Thompson, Daniel C. Integrability and non-integrability in $N = 2$ SCFTs and their holographic backgrounds, Journal of High Energy Physics, Volume 2018 (2018) no. 7 | DOI:10.1007/jhep07(2018)044
Yagasaki, Kazuyuki Nonintegrability of the unfolding of the fold-Hopf bifurcation, Nonlinearity, Volume 31 (2018) no. 2, p. 341 | DOI:10.1088/1361-6544/aa92e8
Casale, Guy; Weil, Jacques-Arthur Galoisian methods for testing irreducibility of order two nonlinear differential equations, Pacific Journal of Mathematics, Volume 297 (2018) no. 2, p. 299 | DOI:10.2140/pjm.2018.297.299
Yamanaka, Shogo Local Integrability of Poincaré–Dulac Normal Forms, Regular and Chaotic Dynamics, Volume 23 (2018) no. 7-8, p. 933 | DOI:10.1134/s1560354718070080
Remy, Pascal Resurgence and highest level’s connection-to-Stokes formulæ for some linear meromorphic differential systems, Annales de la Faculté des sciences de Toulouse : Mathématiques, Volume 26 (2017) no. 3, p. 645 | DOI:10.5802/afst.1548
Maciejewski, Andrzej J.; Przybylska, Maria; Szumiński, Wojciech Anisotropic Kepler and anisotropic two fixed centres problems, Celestial Mechanics and Dynamical Astronomy, Volume 127 (2017) no. 2, p. 163 | DOI:10.1007/s10569-016-9722-z
Benner, Peter; Denißen, Jonas; Kohaupt, Ludwig Trigonometric spline and spectral bounds for the solution of linear time-periodic systems, Journal of Applied Mathematics and Computing, Volume 54 (2017) no. 1-2, p. 127 | DOI:10.1007/s12190-016-1001-3
Aparicio-Monforte, A.; Dreyfus, T.; Weil, J.-A. Liouville integrability: An effective Morales–Ramis–Simó theorem, Journal of Symbolic Computation, Volume 74 (2016), p. 537 | DOI:10.1016/j.jsc.2015.08.009
Rein, Hanno; Tamayo, Daniel Second-order variational equations forN-body simulations, Monthly Notices of the Royal Astronomical Society, Volume 459 (2016) no. 3, p. 2275 | DOI:10.1093/mnras/stw644
Maciejewski, Andrzej J.; Przybylska, Maria Integrability of Hamiltonian systems with algebraic potentials, Physics Letters A, Volume 380 (2016) no. 1-2, p. 76 | DOI:10.1016/j.physleta.2015.08.035
Combot, Thierry Integrability and Non Integrability of Some n Body Problems, Recent Advances in Celestial and Space Mechanics, Volume 23 (2016), p. 1 | DOI:10.1007/978-3-319-27464-5_1
Christov, Ognyan; Georgiev, Georgi On the integrability of a system describing the stationary solutions in Bose–Fermi mixtures, Chaos, Solitons Fractals, Volume 77 (2015), p. 138 | DOI:10.1016/j.chaos.2015.05.024
Morales-Ruiz, Juan J. Picard–Vessiot theory and integrability, Journal of Geometry and Physics, Volume 87 (2015), p. 314 | DOI:10.1016/j.geomphys.2014.07.006
Jahn, Jiří; Jahnová, Jiřina Towards the proof of Yoshida’s conjecture, Nonlinearity, Volume 28 (2015) no. 9, p. 3389 | DOI:10.1088/0951-7715/28/9/3389
Llibre, Jaume; Valls, Claudia Analytic integrability of Hamiltonian systems with exceptional potentials, Physics Letters A, Volume 379 (2015) no. 38, p. 2295 | DOI:10.1016/j.physleta.2015.07.034
Simó, Carles Measuring the total amount of chaos in some Hamiltonian systems, Discrete Continuous Dynamical Systems - A, Volume 34 (2014) no. 12, p. 5135 | DOI:10.3934/dcds.2014.34.5135
Li, Wenlei; Shi, Shaoyun Weak-Painlevé property and integrability of general dynamical systems, Discrete Continuous Dynamical Systems - A, Volume 34 (2014) no. 9, p. 3667 | DOI:10.3934/dcds.2014.34.3667
Maciejewski, Andrzej J.; Duval, Guillaume Integrability of Hamiltonian systems with homogeneous potentials of degrees $\pm 2$ . An application of higher order variational equations, Discrete and Continuous Dynamical Systems, Volume 34 (2014) no. 11, p. 4589 | DOI:10.3934/dcds.2014.34.4589
Simon, Sergi Linearised higher variational equations, Discrete and Continuous Dynamical Systems, Volume 34 (2014) no. 11, p. 4827 | DOI:10.3934/dcds.2014.34.4827
Giataganas, Dimitrios; Zayas, Leopoldo A. Pando; Zoubos, Konstantinos On marginal deformations and non-integrability, Journal of High Energy Physics, Volume 2014 (2014) no. 1 | DOI:10.1007/jhep01(2014)129
VAN MINH, Nguyen; ZUNG, Nguyen Tien Geometry of nondegenerate $R^{n}$ -actions on $n$ -manifolds, Journal of the Mathematical Society of Japan, Volume 66 (2014) no. 3 | DOI:10.2969/jmsj/06630839
Stoyanova, Tsvetana Non-integrability of the fourth Painlevé equation in the Liouville–Arnold sense, Nonlinearity, Volume 27 (2014) no. 5, p. 1029 | DOI:10.1088/0951-7715/27/5/1029
Bostan, Alin; Combot, Thierry; El Din, Mohab Safey, Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation (2014), p. 67 | DOI:10.1145/2608628.2608662
Combot, Thierry A note on algebraic potentials and Morales–Ramis theory, Celestial Mechanics and Dynamical Astronomy, Volume 115 (2013) no. 4, p. 397 | DOI:10.1007/s10569-013-9470-2
B. Acosta-Humánez, Primitivo; Alvarez-Ramírez, Martha; Blázquez-Sanz, David; Delgado, Joaquín Non-integrability criterium for normal variational equations around an integrable subsystem and an example: The Wilberforce spring-pendulum, Discrete Continuous Dynamical Systems - A, Volume 33 (2013) no. 3, p. 965 | DOI:10.3934/dcds.2013.33.965
Shi, Shaoyun; Li, Wenlei Non-integrability of generalized Yang-Mills Hamiltonian system, Discrete Continuous Dynamical Systems - A, Volume 33 (2013) no. 4, p. 1645 | DOI:10.3934/dcds.2013.33.1645
Stepanchuk, A; Tseytlin, A A On (non)integrability of classical strings inp-brane backgrounds, Journal of Physics A: Mathematical and Theoretical, Volume 46 (2013) no. 12, p. 125401 | DOI:10.1088/1751-8113/46/12/125401
Combot, Thierry Integrability conditions at order 2 for homogeneous potentials of degree −1, Nonlinearity, Volume 26 (2013) no. 1, p. 95 | DOI:10.1088/0951-7715/26/1/95
Christov, Ognyan Non-integrability of first order resonances in Hamiltonian systems in three degrees of freedom, Celestial Mechanics and Dynamical Astronomy, Volume 112 (2012) no. 2, p. 149 | DOI:10.1007/s10569-011-9389-4
Combot, Thierry Non-integrability of the equal mass n-body problem with non-zero angular momentum, Celestial Mechanics and Dynamical Astronomy, Volume 114 (2012) no. 4, p. 319 | DOI:10.1007/s10569-012-9417-z
Blázquez-Sanz, David; J. Morales-Ruiz, Juan Lie's reduction method and differential Galois theory in the complex analytic context, Discrete Continuous Dynamical Systems - A, Volume 32 (2012) no. 2, p. 353 | DOI:10.3934/dcds.2012.32.353
Blázquez-Sanz, David; Yagasaki, Kazuyuki Analytic and algebraic conditions for bifurcations of homoclinic orbits I: Saddle equilibria, Journal of Differential Equations, Volume 253 (2012) no. 11, p. 2916 | DOI:10.1016/j.jde.2012.08.008
Basu, Pallab; Das, Diptarka; Ghosh, Archisman; Zayas, Leopoldo A. Pando Chaos around holographic Regge trajectories, Journal of High Energy Physics, Volume 2012 (2012) no. 5 | DOI:10.1007/jhep05(2012)077
Llibre, Jaume; Vidal, Claudio Periodic orbits and non-integrability in a cosmological scalar field, Journal of Mathematical Physics, Volume 53 (2012) no. 1 | DOI:10.1063/1.3675493
Ben Hamed, Bassem; Gavrilov, Lubomir; Klughertz, Martine The holonomy group at infinity of the Painlevé VI equation, Journal of Mathematical Physics, Volume 53 (2012) no. 2 | DOI:10.1063/1.3681897
Combot, Thierry; Koutschan, Christoph Third order integrability conditions for homogeneous potentials of degree −1, Journal of Mathematical Physics, Volume 53 (2012) no. 8 | DOI:10.1063/1.4746691
Aparicio-Monforte, Ainhoa; Weil, Jacques-Arthur A reduced form for linear differential systems and its application to integrability of Hamiltonian systems, Journal of Symbolic Computation, Volume 47 (2012) no. 2, p. 192 | DOI:10.1016/j.jsc.2011.09.011
Liu Chang; Guo Yong-Xin; Liu Shi-Xing Discrete variational calculation of Hénon-Heiles equation in the Birkhoffian sense, Acta Physica Sinica, Volume 60 (2011) no. 6, p. 064501 | DOI:10.7498/aps.60.064501
Stoyanova, Tsvetana Non-Integrability of Painlevé V Equations in the Liouville Sense and Stokes Phenomenon, Advances in Pure Mathematics, Volume 01 (2011) no. 04, p. 170 | DOI:10.4236/apm.2011.14031
Li, Wenlei; Shi, Shaoyun Non-integrability of Hénon-Heiles system, Celestial Mechanics and Dynamical Astronomy, Volume 109 (2011) no. 1, p. 1 | DOI:10.1007/s10569-010-9315-1
Li, Wenlei; Shi, Shaoyun; Liu, Bing Non-integrability of a class of Hamiltonian systems, Journal of Mathematical Physics, Volume 52 (2011) no. 11 | DOI:10.1063/1.3659284
Llibre, Jaume; Jiménez-Lara, Lidia Periodic orbits and non-integrability of Hénon–Heiles systems, Journal of Physics A: Mathematical and Theoretical, Volume 44 (2011) no. 20, p. 205103 | DOI:10.1088/1751-8113/44/20/205103
Basu, Pallab; Pando Zayas, Leopoldo A. Analytic nonintegrability in string theory, Physical Review D, Volume 84 (2011) no. 4 | DOI:10.1103/physrevd.84.046006
Ayoul, Michaël; Zung, Nguyen Tien Galoisian obstructions to non-Hamiltonian integrability, Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, p. 1323 | DOI:10.1016/j.crma.2010.10.024
Casale, G.; Roques, J. Dynamics of Rational Symplectic Mappings and Difference Galois Theory, International Mathematics Research Notices (2010) | DOI:10.1093/imrn/rnn103
Blázquez-Sanz, D.; Carrillo Torres, S. A. Group analysis of non-autonomous linear Hamiltonians through differential Galois theory, Lobachevskii Journal of Mathematics, Volume 31 (2010) no. 2, p. 157 | DOI:10.1134/s1995080210020071
Morikawa, Shuji; Saito, Katsunori; Takeuchi, Taihei; Umemura, Hiroshi Discrete Burgers’ Equation, Binomial Coefficients and Mandala, Mathematics in Computer Science, Volume 4 (2010) no. 2-3, p. 151 | DOI:10.1007/s11786-010-0049-y
Pujol, O.; Pérez, J.P.; Ramis, J.P.; Simó, C.; Simon, S.; Weil, J.A. Swinging Atwood Machine: Experimental and numerical results, and a theoretical study, Physica D: Nonlinear Phenomena, Volume 239 (2010) no. 12, p. 1067 | DOI:10.1016/j.physd.2010.02.017
MACIEJEWSKI, ANDRZEJ J.; PRZYBYLSKA, MARIA DIFFERENTIAL GALOIS THEORY AND INTEGRABILITY, International Journal of Geometric Methods in Modern Physics, Volume 06 (2009) no. 08, p. 1357 | DOI:10.1142/s0219887809004272
Stoyanova, Tsvetana Non-integrability of Painlevé VI equations in the Liouville sense, Nonlinearity, Volume 22 (2009) no. 9, p. 2201 | DOI:10.1088/0951-7715/22/9/008
Nomikos, D.G.; Papageorgiou, V.G. Non-integrability of the Anisotropic Stormer Problem and the Isosceles Three-Body Problem, Physica D: Nonlinear Phenomena, Volume 238 (2009) no. 3, p. 273 | DOI:10.1016/j.physd.2008.10.010
Acosta-Humánez, Primitivo B.; Álvarez-Ramírez, Martha; Delgado, Joaquín Non-Integrability of Some Few Body Problems in Two Degrees of Freedom, Qualitative Theory of Dynamical Systems, Volume 8 (2009) no. 2, p. 209 | DOI:10.1007/s12346-010-0008-7
Przybylska, M. Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedom, Regular and Chaotic Dynamics, Volume 14 (2009) no. 2, p. 263 | DOI:10.1134/s1560354709020063
Martínez, R.; Simó, C. Non-integrability of Hamiltonian systems through high order variational equations: Summary of results and examples, Regular and Chaotic Dynamics, Volume 14 (2009) no. 3, p. 323 | DOI:10.1134/s1560354709030010
Przybylska, M. Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedom. Nongeneric cases, Regular and Chaotic Dynamics, Volume 14 (2009) no. 3, p. 349 | DOI:10.1134/s1560354709030022
Maciejewski, Andrzej J; Przybylska, Maria; Stachowiak, Tomasz; Szydłowski, Marek Global integrability of cosmological scalar fields, Journal of Physics A: Mathematical and Theoretical, Volume 41 (2008) no. 46, p. 465101 | DOI:10.1088/1751-8113/41/46/465101

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