A new proof of Poincar\'e's result on the restricted three-body problem
暂无分享,去创建一个
[1] J. Ramis,et al. GALOISIAN OBSTRUCTIONS TO INTEGRABILITY OF HAMILTONIAN SYSTEMS: STATEMENTS AND EXAMPLES , 1999 .
[2] J. Vrbik. New Methods of Celestial Mechanics , 2018 .
[3] Thierry Combot. A note on algebraic potentials and Morales–Ramis theory , 2012, 1209.4747.
[4] Henri Poincaré,et al. On the Three-body Problem and the Equations of Dynamics , 2017 .
[5] N. T. Zung,et al. A Conceptual Approach to the Problem of Action-Angle Variables , 2017, 1706.08859.
[6] Jaume Llibre,et al. Oscillatory solutions in the planar restricted three-body problem , 1980 .
[7] K. Tamvakis. Symmetries , 2019, Undergraduate Texts in Physics.
[8] Kazuyuki Yagasaki. Nonintegrability of nearly integrable dynamical systems near resonant periodic orbits , 2021 .
[9] V. Arnold,et al. Dynamical Systems III: Mathematical Aspects of Classical and Celestial Mechanics , 1989 .
[10] A. Tsygvintsev. Non-Existence of New Meromorphic First Integrals in the Planar Three-Body Problem , 2002 .
[11] P. Martín,et al. Oscillatory motions for the restricted planar circular three body problem , 2012, 1506.04551.
[12] C. Simó,et al. Integrability of hamiltonian systems and differential Galois groups of higher variational equations , 2007 .
[13] Kazuyuki Yagasaki,et al. Non-integrability of the restricted three-body problem , 2021, Ergodic Theory and Dynamical Systems.
[14] Edmund Taylor Whittaker,et al. A treatise on the analytical dynamics of particles and rigid bodies , 1927 .
[15] J. Barrow-Green. Poincare and the Three Body Problem , 1996 .
[16] Alexei Tsygvintsev. La non-int'egrabilit'e m'eromorphe du probl`eme plan des trois corps , 2000 .
[17] On some exceptional cases in the integrability of the three-body problem , 2006, math/0610951.
[18] Gorjan Alagic,et al. #p , 2019, Quantum information & computation.
[19] J. Morales-Ruiz,et al. ON THE MEROMORPHIC NON-INTEGRABILITY OF SOME N-BODY PROBLEMS , 2009 .
[20] D. Saari,et al. Stable and Random Motions in Dynamical Systems , 1975 .
[21] Nguyen Tien Zung,et al. Galoisian obstructions to non-Hamiltonian integrability , 2009 .
[22] V. Arnold. Mathematical Methods of Classical Mechanics , 1974 .
[23] Valerii V Kozlov,et al. Integrability and non-integrability in Hamiltonian mechanics , 1983 .
[24] Kenneth R. Meyer,et al. Introduction to Hamiltonian Dynamical Systems and the N-Body Problem , 1991 .
[25] Juan José Morales Ruiz,et al. Differential Galois Theory and Non-Integrability of Hamiltonian Systems , 1999 .
[26] Oleg I. Bogoyavlenskij,et al. Extended Integrability and Bi-Hamiltonian Systems , 1998 .
[27] The meromorphic non-integrability of the three-body problem , 2000, math/0009218.