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Volumn 38, Issue 24, 2005, Pages

Lagrangian submanifolds and dynamics on Lie algebroids

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EID: 19844361844     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/38/24/R01     Document Type: Review
Times cited : (159)

References (50)
  • 4
    • 0037909707 scopus 로고    scopus 로고
    • Poisson sigma models and symplectic groupoids
    • Cattaneo A S and Felder G 2001 Poisson sigma models and symplectic groupoids Quantization of Singular Symplectic Quotients (Progress in Mathematics vol 198) ed N P Landsman, M Pflaum and M Schlichenmeier pp 41-73
    • (2001) Quantization of Singular Symplectic Quotients , pp. 41-73
    • Cattaneo, A.S.1    Felder, G.2
  • 5
    • 19844374964 scopus 로고    scopus 로고
    • Variational principles for Lie-Poisson and Hamilton-Poincaré equations
    • Cendra H, Marden J E, Pekarsky S and Ratiu T S 2003 Variational principles for Lie-Poisson and Hamilton-Poincaré equations Mosc. Math. J. 3 833-67
    • (2003) Mosc. Math. J. , vol.3 , pp. 833-867
    • Cendra, H.1    Marden, J.E.2    Pekarsky, S.3    Ratiu, T.S.4
  • 8
    • 8644241816 scopus 로고    scopus 로고
    • Mechanical control systems on Lie algebroids
    • Cortés J and Martínez E 2004 Mechanical control systems on Lie algebroids IMA J. Math. Control Inf. 21 457-92
    • (2004) IMA J. Math. Control Inf. , vol.21 , Issue.4 , pp. 457-492
    • Cortés, J.1    Martínez, E.2
  • 11
    • 4644362873 scopus 로고    scopus 로고
    • Integrability of Poisson brackets
    • Crainic M and Fernandes R L 2004 Integrability of Poisson brackets J. Diff. Geom. 66 71-137
    • (2004) J. Diff. Geom. , vol.66 , pp. 71-137
    • Crainic, M.1    Fernandes, R.L.2
  • 13
    • 0001576518 scopus 로고    scopus 로고
    • Tangent and cotangent lifts and graded Lie algebras associated with Lie algebroids
    • Grabowski J and Urbański P 1997 Tangent and cotangent lifts and graded Lie algebras associated with Lie algebroids Ann. Global Anal. Geom. 15 447-86
    • (1997) Ann. Global Anal. Geom. , vol.15 , Issue.5 , pp. 447-486
    • Grabowski, J.1    Urbański, P.2
  • 14
    • 0031257829 scopus 로고    scopus 로고
    • Lie algebroids and Poisson-Nijenhuis structures
    • Grabowski J and Urbański P 1997 Lie algebroids and Poisson-Nijenhuis structures Rep. Math. Phys. 40 195-208
    • (1997) Rep. Math. Phys. , vol.40 , Issue.2 , pp. 195-208
    • Grabowski, J.1    Urbański, P.2
  • 16
    • 9144240076 scopus 로고    scopus 로고
    • AV-differential geometry: Poisson and Jacobi structures
    • Grabowska K, Grabowski J and Urbański P 2004 AV-differential geometry: Poisson and Jacobi structures J. Geom. Phys. 52 398-446
    • (2004) J. Geom. Phys. , vol.52 , Issue.4 , pp. 398-446
    • Grabowska, K.1    Grabowski, J.2    Urbański, P.3
  • 17
    • 0000855801 scopus 로고
    • Algebraic constructions in the category of Lie algebroids
    • Higgins P J and Mackenzie K 1990 Algebraic constructions in the category of Lie algebroids J. Algebra 129 194-230
    • (1990) J. Algebra , vol.129 , Issue.1 , pp. 194-230
    • Higgins, P.J.1    MacKenzie, K.2
  • 19
    • 0002761713 scopus 로고
    • Espaces variationnels et mécanique
    • Klein J 1962 Espaces variationnels et mécanique Ann. Inst. Fourier 12 1-124
    • (1962) Ann. Inst. Fourier , vol.12 , pp. 1-124
    • Klein, J.1
  • 23
    • 0001015316 scopus 로고    scopus 로고
    • Lie algebroids and mechanics
    • Libermann P 1996 Lie algebroids and mechanics Arch. Math. (Brno) 32 147-62
    • (1996) Arch. Math. (Brno) , vol.32 , pp. 147-162
    • Libermann, P.1
  • 26
    • 84973999707 scopus 로고
    • Lie bialgebroids and Poisson groupoids
    • Mackenzie K and Xu P 1994 Lie bialgebroids and Poisson groupoids Duke Math. J. 73 415-52
    • (1994) Duke Math. J. , vol.73 , Issue.2 , pp. 415-452
    • MacKenzie, K.1    Xu, P.2
  • 29
    • 0035385190 scopus 로고    scopus 로고
    • Lagrangian mechanics on Lie algebroids
    • Martínez E 2001 Lagrangian mechanics on Lie algebroids Acta Appl. Math. 67 295-20
    • (2001) Acta Appl. Math. , vol.67 , Issue.3 , pp. 295-320
    • Martínez, E.1
  • 30
    • 8644261436 scopus 로고    scopus 로고
    • Geometric formulation of mechanics on Lie algebroids
    • Martínez E 2001 Geometric formulation of mechanics on Lie algebroids Proc. 8th Fall Workshop on Geometry and Physics (Medina del Campo, 1999) vol 2 ((Publicaciones de la RSME)) pp 209-22
    • (2001) Proc. 8th Fall Workshop on Geometry and Physics , vol.2 , pp. 209-222
    • Martínez, E.1
  • 31
    • 12144290974 scopus 로고    scopus 로고
    • Reduction of optimal control systems
    • Martínez E 2004 Reduction of optimal control systems Rep. Math. Phys. 53 79-90
    • (2004) Rep. Math. Phys. , vol.53 , Issue.1 , pp. 79-90
    • Martínez, E.1
  • 32
    • 19844363095 scopus 로고    scopus 로고
    • Lie algebroids, some generalizations and applications
    • Martínez E 2002 Lie algebroids, some generalizations and applications Proc. 11th Fall Workshop on Geometry and Physics (Oviedo) vol 6 ((Publicaciones de la RSME)) pp 103-17
    • (2002) Proc. 11th Fall Workshop on Geometry and Physics , vol.6 , pp. 103-117
    • Martínez, E.1
  • 35
    • 0036837579 scopus 로고    scopus 로고
    • Lie algebroid structures and Lagrangian systems on affine bundles
    • Martínez E, Mestdag T and Sarlet W 2002 Lie algebroid structures and Lagrangian systems on affine bundles J. Geom. Phys. 44 70-95
    • (2002) J. Geom. Phys. , vol.44 , Issue.1 , pp. 70-95
    • Martínez, E.1    Mestdag, T.2    Sarlet, W.3
  • 36
    • 13744264182 scopus 로고    scopus 로고
    • A Lie algebroid framework for non-holonomic systems
    • Mestdag T and Langerock B 2005 A Lie algebroid framework for non-holonomic systems J. Phys. A: Math. Gen. 38 1097-111
    • (2005) J. Phys. A: Math. Gen. , vol.38 , Issue.5 , pp. 1097-1111
    • Mestdag, T.1    Langerock, B.2
  • 37
    • 0003189635 scopus 로고
    • Canonical formulations of a particle in a Yang-Mills field
    • Montgomery R 1984 Canonical formulations of a particle in a Yang-Mills field Lett. Math. Phys. 8 59-67
    • (1984) Lett. Math. Phys. , vol.8 , Issue.1 , pp. 59-67
    • Montgomery, R.1
  • 38
    • 0001361507 scopus 로고
    • Isoholonomics problems and some applications
    • Montgomery R 1990 Isoholonomics problems and some applications Commun. Math. Phys. 128 565-92
    • (1990) Commun. Math. Phys. , vol.128 , pp. 565-592
    • Montgomery, R.1
  • 39
    • 0007075930 scopus 로고
    • Gauge theory of the falling cat
    • Montgomery R 1993 Gauge theory of the falling cat Fields Inst. Commun. 1 193-218
    • (1993) Fields Inst. Commun. , vol.1 , pp. 193-218
    • Montgomery, R.1
  • 41
    • 0036850829 scopus 로고    scopus 로고
    • Lie algebroid structures on a class of affine bundles
    • Sarlet W, Mestdag T and Martínez E 2002 Lie algebroid structures on a class of affine bundles J. Math. Phys. 43 5654-74
    • (2002) J. Math. Phys. , vol.43 , Issue.11 , pp. 5654-5674
    • Sarlet, W.1    Mestdag, T.2    Martínez, E.3
  • 42
    • 4644257092 scopus 로고    scopus 로고
    • Prolongations of Lie groupoids and Lie algebroids
    • Saunders D 2004 Prolongations of Lie groupoids and Lie algebroids Houst. J. Math. 30 637-55
    • (2004) Houst. J. Math. , vol.30 , pp. 637-655
    • Saunders, D.1
  • 44
    • 84968475624 scopus 로고
    • Orbits of families of vector fields and integrability of distributions
    • Sussmann H J 1973 Orbits of families of vector fields and integrability of distributions Trans. Am. Math. Soc. 180 171-88
    • (1973) Trans. Am. Math. Soc. , vol.180 , pp. 171-188
    • Sussmann, H.J.1
  • 45
    • 0038385998 scopus 로고
    • Les sous-variétés lagrangiennes et la dynamique hamiltonienne
    • Tulczyjew W 1976 Les sous-variétés lagrangiennes et la dynamique hamiltonienne C. R. Acad. Sci., Paris 283 15-8
    • (1976) C. R. Acad. Sci., Paris , vol.283 , pp. 15-18
    • Tulczyjew, W.1
  • 46
    • 0039023076 scopus 로고
    • Les sous-variétés lagrangiennes et la dynamique lagrangienne
    • Tulczyjew W 1976 Les sous-variétés lagrangiennes et la dynamique lagrangienne C. R. Acad. Sci., Paris 283 675-8
    • (1976) C. R. Acad. Sci., Paris , vol.283 , pp. 675-678
    • Tulczyjew, W.1
  • 49
    • 84968464920 scopus 로고
    • Symplectic groupoids and Poisson manifolds
    • Weinstein A 1987 Symplectic groupoids and Poisson manifolds Bull. (New Ser.) Am. Math. Soc. 16 101-4
    • (1987) Bull. (New Ser.) Am. Math. Soc. , vol.16 , pp. 101-104
    • Weinstein, A.1
  • 50
    • 0000714030 scopus 로고    scopus 로고
    • Lagrangian mechanics and groupoids
    • Weinstein A 1996 Lagrangian mechanics and groupoids Fields Inst. Commun. 7 207-31
    • (1996) Fields Inst. Commun. , vol.7 , pp. 207-231
    • Weinstein, A.1


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