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Symplectic groupoids and discrete constrained Lagrangian mechanics
1. | Unidad Asociada ULL-CSIC "Geometría Diferencial y Mecánica Geométrica", Departamento de Matemática Fundamental, Facultad de Matemáticas, Universidad de la Laguna, La Laguna, Tenerife, Canary Islands, Spain |
2. | Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, Campus de Cantoblanco, UAM, C/Nicolás Cabrera, 15, 28049 Madrid |
3. | Department of Mathematics, Washington University in St. Louis, Campus Box 1146, One Brookings Drive, St. Louis, Missouri 63130-4899, United States |
References:
[1] |
2nd edition, Applied Mathematical Sciences, 75, Springer-Verlag, New York, 1988.
doi: 10.1007/978-1-4612-1029-0. |
[2] |
Found. Comput. Math., 9 (2009), 197-219.
doi: 10.1007/s10208-008-9030-4. |
[3] |
Berkeley Mathematics Lecture Notes, 10, American Mathematical Society, Providence, RI, 1999. Google Scholar |
[4] |
in Publications du Département de Mathématiques. Nouvelle Série. A, Vol. 2, Publ. Dép. Math. Nouvelle Sér. A, 87, Univ. Claude-Bernard, Lyon, 1987, i-ii, 1-62. |
[5] |
Indiana Univ. Math. J., 39 (1990), 859-876.
doi: 10.1512/iumj.1990.39.39042. |
[6] |
2nd edition, Springer Series in Computational Mathematics, 31, Springer-Verlag, Berlin, 2006,. Google Scholar |
[7] |
Dyn. Syst., 23 (2008), 351-397.
doi: 10.1080/14689360802294220. |
[8] |
J. Math. Phys., 40 (1999), 3353-3371.
doi: 10.1063/1.532892. |
[9] |
SIAM J. Control Optim., 35 (1997), 901-929.
doi: 10.1137/S0363012995290367. |
[10] |
Translated from the French by Bertram Eugene Schwarzbach, Mathematics and its Applications, 35, D. Reidel Publishing Co., Dordrecht, 1987. Google Scholar |
[11] |
London Mathematical Society Lecture Note Series, 213, Cambridge University Press, Cambridge, 2005.
doi: 10.1017/CBO9781107325883. |
[12] |
in The Breadth of Symplectic and Poisson Geometry, Progr. Math., 232, Birkhäuser Boston, Boston, MA, 2005, 493-523.
doi: 10.1007/0-8176-4419-9\_17. |
[13] |
Nonlinearity, 19 (2006), 1313-1348; Corrigendum, Nonlinearity, 19 (2006), 3003-3004.
doi: 10.1088/0951-7715/19/6/006. |
[14] |
J. C. Marrero, D. Martín de Diego and E. Martínez, The exact discrete Lagrangian function on Lie groupoids and some applications,, in preparation., (). Google Scholar |
[15] |
Acta Numer., 10 (2001), 357-514.
doi: 10.1017/S096249290100006X. |
[16] |
in Integration Algorithms and Classical Mechanics (Toronto, ON, 1993), Fields Inst. Commun., 10, Amer. Math. Soc., Providence, RI, 1996, 151-180. |
[17] |
Comm. Math. Phys., 139 (1991), 217-243.
doi: 10.1007/BF02352494. |
[18] |
Indiana Univ. Math. J., 22 (1972), 267-275.
doi: 10.1512/iumj.1973.22.22021. |
[19] |
J. Symplectic Geom., 8 (2010), 225-238.
doi: 10.4310/JSG.2010.v8.n2.a5. |
[20] |
Mat. Model., 2 (1990), 78-87. |
[21] |
Ann. Inst. H. Poincaré Sect. A (N.S.), 27 (1977), 101-114. |
[22] |
J. Math. Soc. Japan, 40 (1988), 705-727.
doi: 10.2969/jmsj/04040705. |
[23] |
in Mechanics Day (Waterloo, ON, 1992), Fields Inst. Commun., 7, American Mathematical Society, Providence, RI, 1996, 207-231. |
[24] |
Internat. J. Math., 6 (1995), 101-124.
doi: 10.1142/S0129167X95000080. |
[25] |
J. Geom. Phys., 57 (2006), 209-250.
doi: 10.1016/j.geomphys.2006.02.012. |
show all references
References:
[1] |
2nd edition, Applied Mathematical Sciences, 75, Springer-Verlag, New York, 1988.
doi: 10.1007/978-1-4612-1029-0. |
[2] |
Found. Comput. Math., 9 (2009), 197-219.
doi: 10.1007/s10208-008-9030-4. |
[3] |
Berkeley Mathematics Lecture Notes, 10, American Mathematical Society, Providence, RI, 1999. Google Scholar |
[4] |
in Publications du Département de Mathématiques. Nouvelle Série. A, Vol. 2, Publ. Dép. Math. Nouvelle Sér. A, 87, Univ. Claude-Bernard, Lyon, 1987, i-ii, 1-62. |
[5] |
Indiana Univ. Math. J., 39 (1990), 859-876.
doi: 10.1512/iumj.1990.39.39042. |
[6] |
2nd edition, Springer Series in Computational Mathematics, 31, Springer-Verlag, Berlin, 2006,. Google Scholar |
[7] |
Dyn. Syst., 23 (2008), 351-397.
doi: 10.1080/14689360802294220. |
[8] |
J. Math. Phys., 40 (1999), 3353-3371.
doi: 10.1063/1.532892. |
[9] |
SIAM J. Control Optim., 35 (1997), 901-929.
doi: 10.1137/S0363012995290367. |
[10] |
Translated from the French by Bertram Eugene Schwarzbach, Mathematics and its Applications, 35, D. Reidel Publishing Co., Dordrecht, 1987. Google Scholar |
[11] |
London Mathematical Society Lecture Note Series, 213, Cambridge University Press, Cambridge, 2005.
doi: 10.1017/CBO9781107325883. |
[12] |
in The Breadth of Symplectic and Poisson Geometry, Progr. Math., 232, Birkhäuser Boston, Boston, MA, 2005, 493-523.
doi: 10.1007/0-8176-4419-9\_17. |
[13] |
Nonlinearity, 19 (2006), 1313-1348; Corrigendum, Nonlinearity, 19 (2006), 3003-3004.
doi: 10.1088/0951-7715/19/6/006. |
[14] |
J. C. Marrero, D. Martín de Diego and E. Martínez, The exact discrete Lagrangian function on Lie groupoids and some applications,, in preparation., (). Google Scholar |
[15] |
Acta Numer., 10 (2001), 357-514.
doi: 10.1017/S096249290100006X. |
[16] |
in Integration Algorithms and Classical Mechanics (Toronto, ON, 1993), Fields Inst. Commun., 10, Amer. Math. Soc., Providence, RI, 1996, 151-180. |
[17] |
Comm. Math. Phys., 139 (1991), 217-243.
doi: 10.1007/BF02352494. |
[18] |
Indiana Univ. Math. J., 22 (1972), 267-275.
doi: 10.1512/iumj.1973.22.22021. |
[19] |
J. Symplectic Geom., 8 (2010), 225-238.
doi: 10.4310/JSG.2010.v8.n2.a5. |
[20] |
Mat. Model., 2 (1990), 78-87. |
[21] |
Ann. Inst. H. Poincaré Sect. A (N.S.), 27 (1977), 101-114. |
[22] |
J. Math. Soc. Japan, 40 (1988), 705-727.
doi: 10.2969/jmsj/04040705. |
[23] |
in Mechanics Day (Waterloo, ON, 1992), Fields Inst. Commun., 7, American Mathematical Society, Providence, RI, 1996, 207-231. |
[24] |
Internat. J. Math., 6 (1995), 101-124.
doi: 10.1142/S0129167X95000080. |
[25] |
J. Geom. Phys., 57 (2006), 209-250.
doi: 10.1016/j.geomphys.2006.02.012. |
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