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On the meromorphic non-integrability of some $N$-body problems
1. | Departamento de Matemática e Informática Aplicadas a la Ingeniería Civil, ETSI Caminos, Canales y Puertos, Universidad Politécnica de Madrid, Profesor Aranguren s/n (Ciudad Universitaria) - 28040 Madrid, Spain |
2. | Département Maths Informatique, Université de Limoges, XLIM - UMR CNRS n. 6172, 123, avenue Albert Thomas - 87060 Limoges, France |
[1] |
Robert I. McLachlan, Ander Murua. The Lie algebra of classical mechanics. Journal of Computational Dynamics, 2019, 6 (2) : 345-360. doi: 10.3934/jcd.2019017 |
[2] |
Eliot Fried. New insights into the classical mechanics of particle systems. Discrete and Continuous Dynamical Systems, 2010, 28 (4) : 1469-1504. doi: 10.3934/dcds.2010.28.1469 |
[3] |
Jaume Llibre, Claudia Valls. On the analytic integrability of the Liénard analytic differential systems. Discrete and Continuous Dynamical Systems - B, 2016, 21 (2) : 557-573. doi: 10.3934/dcdsb.2016.21.557 |
[4] |
Jaume Llibre, Claudia Valls. Analytic integrability of a class of planar polynomial differential systems. Discrete and Continuous Dynamical Systems - B, 2015, 20 (8) : 2657-2661. doi: 10.3934/dcdsb.2015.20.2657 |
[5] |
Sebastián Donoso, Wenbo Sun. Dynamical cubes and a criteria for systems having product extensions. Journal of Modern Dynamics, 2015, 9: 365-405. doi: 10.3934/jmd.2015.9.365 |
[6] |
Jaume Llibre, Yuzhou Tian. Meromorphic integrability of the Hamiltonian systems with homogeneous potentials of degree -4. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021228 |
[7] |
Alessandra Celletti. Some KAM applications to Celestial Mechanics. Discrete and Continuous Dynamical Systems - S, 2010, 3 (4) : 533-544. doi: 10.3934/dcdss.2010.3.533 |
[8] |
Mark A. Pinsky, Alexandr A. Zevin. Stability criteria for linear Hamiltonian systems with uncertain bounded periodic coefficients. Discrete and Continuous Dynamical Systems, 2005, 12 (2) : 243-250. doi: 10.3934/dcds.2005.12.243 |
[9] |
Wenlei Li, Shaoyun Shi. Weak-Painlevé property and integrability of general dynamical systems. Discrete and Continuous Dynamical Systems, 2014, 34 (9) : 3667-3681. doi: 10.3934/dcds.2014.34.3667 |
[10] |
Abed Bounemoura, Edouard Pennamen. Instability for a priori unstable Hamiltonian systems: A dynamical approach. Discrete and Continuous Dynamical Systems, 2012, 32 (3) : 753-793. doi: 10.3934/dcds.2012.32.753 |
[11] |
Thomas Hagen, Andreas Johann, Hans-Peter Kruse, Florian Rupp, Sebastian Walcher. Dynamical systems and geometric mechanics: A special issue in Honor of Jürgen Scheurle. Discrete and Continuous Dynamical Systems - S, 2020, 13 (4) : i-iii. doi: 10.3934/dcdss.20204i |
[12] |
Guillaume Duval, Andrzej J. Maciejewski. Integrability of Hamiltonian systems with homogeneous potentials of degrees $\pm 2$. An application of higher order variational equations. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4589-4615. doi: 10.3934/dcds.2014.34.4589 |
[13] |
Mitsuru Shibayama. Non-integrability criterion for homogeneous Hamiltonian systems via blowing-up technique of singularities. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 3707-3719. doi: 10.3934/dcds.2015.35.3707 |
[14] |
A. Ghose Choudhury, Partha Guha. Chiellini integrability condition, planar isochronous systems and Hamiltonian structures of Liénard equation. Discrete and Continuous Dynamical Systems - B, 2017, 22 (6) : 2465-2478. doi: 10.3934/dcdsb.2017126 |
[15] |
Paola Loreti, Daniela Sforza. Observability of $N$-dimensional integro-differential systems. Discrete and Continuous Dynamical Systems - S, 2016, 9 (3) : 745-757. doi: 10.3934/dcdss.2016026 |
[16] |
Luis C. García-Naranjo, Mats Vermeeren. Structure preserving discretization of time-reparametrized Hamiltonian systems with application to nonholonomic mechanics. Journal of Computational Dynamics, 2021, 8 (3) : 241-271. doi: 10.3934/jcd.2021011 |
[17] |
Ricardo Miranda Martins. Formal equivalence between normal forms of reversible and hamiltonian dynamical systems. Communications on Pure and Applied Analysis, 2014, 13 (2) : 703-713. doi: 10.3934/cpaa.2014.13.703 |
[18] |
S. Aubry, G. Kopidakis, V. Kadelburg. Variational proof for hard Discrete breathers in some classes of Hamiltonian dynamical systems. Discrete and Continuous Dynamical Systems - B, 2001, 1 (3) : 271-298. doi: 10.3934/dcdsb.2001.1.271 |
[19] |
Shiqing Zhang, Qing Zhou. Nonplanar and noncollision periodic solutions for $N$-body problems. Discrete and Continuous Dynamical Systems, 2004, 10 (3) : 679-685. doi: 10.3934/dcds.2004.10.679 |
[20] |
Viktor Levandovskyy, Gerhard Pfister, Valery G. Romanovski. Evaluating cyclicity of cubic systems with algorithms of computational algebra. Communications on Pure and Applied Analysis, 2012, 11 (5) : 2023-2035. doi: 10.3934/cpaa.2012.11.2023 |
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