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Semi-global symplectic invariants of the Euler top
1. | School of Mathematics and Statistics, The University of Sydney, Sydney, NSW 2006, Australia, Australia |
References:
[1] |
A. V. Bolsinov and H. R. Dullin, On the Euler case in rigid body dynamics and the Jacobi problem, (Russian) Regul. Khaoticheskaya Din., 2 (1997), 13-25. |
[2] |
A. V. Bolsinov and A. T. Fomenko, The geodesic flow of an ellipsoid is orbitally equivalent to the integrable Euler case in the dynamics of a rigid body, Dokl. Akad. Nauk, 339 (1994), 253-296. |
[3] |
A. V. Bolsinov and A. T. Fomenko, "Integrable Hamiltonian Systems: Geometry, Topology, Classification,'' Chapman & Hall/CRC, Boca Raton, FL, 2004.
doi: 10.1201/9780203643426. |
[4] |
W. E. Boyce and R. C. DiPrima, "Elementary Differential Equations and Boundary Value Problems,'' $7^{th}$ edition, John Wiley & Sons, Inc., New York-London-Sydney, 2001. |
[5] |
C. H. Clemens, "A Scrapbook of Complex Curve Theory,'' The University Series in Mathematics, Plenum Press, New York-London, 1980. |
[6] |
R. H. Cushman and L. M. Bates, "Global Aspects of Classical Integrable Systems,'' Birkhäuser Verlag, Basel, 1997.
doi: 10.1007/978-3-0348-8891-2. |
[7] |
J.-P. Dufour, P. Molino and A. Toulet, Classification des systèmes intégrables en dimension $2$ et invariants des modèles de Fomenko, C. R. Acad. Sci. Paris Sér. I Math., 318 (1994), 949-952. |
[8] |
H. R. Dullin and S. Vũ Ngoc, Symplectic invariants near hyperbolic-hyperbolic points, Regular and Chaotic Dynamics, 12 (2007), 689-716.
doi: 10.1134/S1560354707060111. |
[9] |
H. R. Dullin, Semi-global symplectic invariants of the spherical pendulum, Journal of Differential Equations, 254 (2013), 2942-2963.
doi: 10.1016/j.jde.2013.01.018. |
[10] |
H. R. Dullin, P. H. Richter, A. P. Veselov and H. Waalkens, Actions of the Neumann systems via Picard-Fuchs equations, Physica D, 155 (2001), 159-183.
doi: 10.1016/S0167-2789(01)00257-3. |
[11] |
D. D. Holm and J. E. Marsden, The rotor and the pendulum, in "Symplectic Geometry and Mathematical Physics" (Aix-en-Provence, 1990), Progr. Math., 99, Birkhäuser Boston, Boston, MA, (1991), 189-203. |
[12] |
E. Leimanis, "The General Problem of the Motion of Coupled Rigid Bodies about a Fixed Point,'' Springer Tracts in Natural Philosophy, 7, Springer-Verlag, Berlin-Heidelberg, 1965.
doi: 10.1007/978-3-642-88412-2. |
[13] |
J. E. Marsden and T. S. Ratiu, "Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems,'' Texts in Applied Mathematics, 17, Springer-Verlag, New York, 1999.
doi: 10.1007/978-0-387-21792-5. |
[14] |
K. Meyer, G. Hall and D. Offin, "Introduction to Hamiltonian Dynamical Systems and the N-Body Problem,'' Second edition, Applied Mathematical Sciences, 90, Springer, New York, 2009.
doi: 10.1007/978-0-387-09724-4. |
[15] |
S. Vũ Ngoc, On semi-global invariants for focus-focus singularities, Topology, 42 (2003), 365-380.
doi: 10.1016/S0040-9383(01)00026-X. |
[16] |
O. E. Orël, On the nonconjugacy of the Euler case in the dynamics of a rigid body and on the Jacobi problem of geodesics on an ellipsoid, Mat. Zametki, 61 (1997), 252-258.
doi: 10.1007/BF02355730. |
[17] |
George Papadopoulos, "Semi-Global Symplectic Invariants of the Euler Top,'' M.S. thesis, The University of Sydney, 2013. |
[18] |
Anne Toulet, "Classification of Integrable Systems on Two-Dimensional Symplectic Manifolds,'' Ph.D thesis, Montpellier II University, 1996. |
[19] |
Nguyen Tien Zung, Convergence versus integrability in Birkhoff normal form, Annals of Mathematics (2), 161 (2005), 141-156.
doi: 10.4007/annals.2005.161.141. |
show all references
References:
[1] |
A. V. Bolsinov and H. R. Dullin, On the Euler case in rigid body dynamics and the Jacobi problem, (Russian) Regul. Khaoticheskaya Din., 2 (1997), 13-25. |
[2] |
A. V. Bolsinov and A. T. Fomenko, The geodesic flow of an ellipsoid is orbitally equivalent to the integrable Euler case in the dynamics of a rigid body, Dokl. Akad. Nauk, 339 (1994), 253-296. |
[3] |
A. V. Bolsinov and A. T. Fomenko, "Integrable Hamiltonian Systems: Geometry, Topology, Classification,'' Chapman & Hall/CRC, Boca Raton, FL, 2004.
doi: 10.1201/9780203643426. |
[4] |
W. E. Boyce and R. C. DiPrima, "Elementary Differential Equations and Boundary Value Problems,'' $7^{th}$ edition, John Wiley & Sons, Inc., New York-London-Sydney, 2001. |
[5] |
C. H. Clemens, "A Scrapbook of Complex Curve Theory,'' The University Series in Mathematics, Plenum Press, New York-London, 1980. |
[6] |
R. H. Cushman and L. M. Bates, "Global Aspects of Classical Integrable Systems,'' Birkhäuser Verlag, Basel, 1997.
doi: 10.1007/978-3-0348-8891-2. |
[7] |
J.-P. Dufour, P. Molino and A. Toulet, Classification des systèmes intégrables en dimension $2$ et invariants des modèles de Fomenko, C. R. Acad. Sci. Paris Sér. I Math., 318 (1994), 949-952. |
[8] |
H. R. Dullin and S. Vũ Ngoc, Symplectic invariants near hyperbolic-hyperbolic points, Regular and Chaotic Dynamics, 12 (2007), 689-716.
doi: 10.1134/S1560354707060111. |
[9] |
H. R. Dullin, Semi-global symplectic invariants of the spherical pendulum, Journal of Differential Equations, 254 (2013), 2942-2963.
doi: 10.1016/j.jde.2013.01.018. |
[10] |
H. R. Dullin, P. H. Richter, A. P. Veselov and H. Waalkens, Actions of the Neumann systems via Picard-Fuchs equations, Physica D, 155 (2001), 159-183.
doi: 10.1016/S0167-2789(01)00257-3. |
[11] |
D. D. Holm and J. E. Marsden, The rotor and the pendulum, in "Symplectic Geometry and Mathematical Physics" (Aix-en-Provence, 1990), Progr. Math., 99, Birkhäuser Boston, Boston, MA, (1991), 189-203. |
[12] |
E. Leimanis, "The General Problem of the Motion of Coupled Rigid Bodies about a Fixed Point,'' Springer Tracts in Natural Philosophy, 7, Springer-Verlag, Berlin-Heidelberg, 1965.
doi: 10.1007/978-3-642-88412-2. |
[13] |
J. E. Marsden and T. S. Ratiu, "Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems,'' Texts in Applied Mathematics, 17, Springer-Verlag, New York, 1999.
doi: 10.1007/978-0-387-21792-5. |
[14] |
K. Meyer, G. Hall and D. Offin, "Introduction to Hamiltonian Dynamical Systems and the N-Body Problem,'' Second edition, Applied Mathematical Sciences, 90, Springer, New York, 2009.
doi: 10.1007/978-0-387-09724-4. |
[15] |
S. Vũ Ngoc, On semi-global invariants for focus-focus singularities, Topology, 42 (2003), 365-380.
doi: 10.1016/S0040-9383(01)00026-X. |
[16] |
O. E. Orël, On the nonconjugacy of the Euler case in the dynamics of a rigid body and on the Jacobi problem of geodesics on an ellipsoid, Mat. Zametki, 61 (1997), 252-258.
doi: 10.1007/BF02355730. |
[17] |
George Papadopoulos, "Semi-Global Symplectic Invariants of the Euler Top,'' M.S. thesis, The University of Sydney, 2013. |
[18] |
Anne Toulet, "Classification of Integrable Systems on Two-Dimensional Symplectic Manifolds,'' Ph.D thesis, Montpellier II University, 1996. |
[19] |
Nguyen Tien Zung, Convergence versus integrability in Birkhoff normal form, Annals of Mathematics (2), 161 (2005), 141-156.
doi: 10.4007/annals.2005.161.141. |
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