no. 4
The Symplectic Structure of Curves in Three Dimensional Spaces of Constant Curvature and the Equations of Mathematical Physics
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1483-1515. 
@article{AIHPC_2009__26_4_1483_0,
     author = {Jurdjevic, V.},
     title = {The {Symplectic} {Structure} of {Curves} in {Three} {Dimensional} {Spaces} of {Constant} {Curvature} and the {Equations} of {Mathematical} {Physics}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1483--1515},
     publisher = {Elsevier},
     volume = {26},
     number = {4},
     year = {2009},
     doi = {10.1016/j.anihpc.2008.12.006},
     mrnumber = {2542734},
     zbl = {1176.53075},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2008.12.006/}
}
TY  - JOUR
AU  - Jurdjevic, V.
TI  - The Symplectic Structure of Curves in Three Dimensional Spaces of Constant Curvature and the Equations of Mathematical Physics
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
SP  - 1483
EP  - 1515
VL  - 26
IS  - 4
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2008.12.006/
DO  - 10.1016/j.anihpc.2008.12.006
LA  - en
ID  - AIHPC_2009__26_4_1483_0
ER  - 
%0 Journal Article
%A Jurdjevic, V.
%T The Symplectic Structure of Curves in Three Dimensional Spaces of Constant Curvature and the Equations of Mathematical Physics
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 1483-1515
%V 26
%N 4
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpc.2008.12.006/
%R 10.1016/j.anihpc.2008.12.006
%G en
%F AIHPC_2009__26_4_1483_0
Jurdjevic, V. The Symplectic Structure of Curves in Three Dimensional Spaces of Constant Curvature and the Equations of Mathematical Physics. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1483-1515. doi : 10.1016/j.anihpc.2008.12.006. http://www.numdam.org/articles/10.1016/j.anihpc.2008.12.006/

[1] Abraham R., Marsden J., Foundations of Mechanics, Benjamin-Cummings, Reading, MA, 1978. | MR | Zbl

[2] Arnold V. I., Khesin B. A., Topological Methods in Hydrodynamics, Appl. Math. Sci., vol. 125, Springer-Verlag, New York, 1998. | MR | Zbl

[3] Brylinski J. P., Loop Spaces, Characteristic Classes and Geometric Quantization, Progr. Math., vol. 108, Birkhäuser, Boston, 1993. | MR | Zbl

[4] Epstein C. L., Weinstein M. I., A Stable Manifold Theorem for the Curve Shortening Equation, Comm. Pure Appl. Math. XL (1987) 119-139. | MR | Zbl

[5] Faddeev L., Takhtajan L., Hamiltonian Methods in the Theory of Solitons, Springer-Verlag, Berlin, 1980. | Zbl

[6] Hamilton R. S., The Inverse Function Theorem of Nash and Moser, Bull. Amer. Math. Soc. 7 (1972) 65-221. | MR | Zbl

[7] Hasimoto H., Motion of a Vortex Filament and Its Relation to Elastica, J. Phys. Soc. Japan 31 (1971) 293-294.

[8] Hasimoto H., A Soliton on a Vortex Filament, J. Fluid Mech. 51 (1972) 477-485. | Zbl

[9] Ivey T., Singer D. A., Knot Types, Homotopies and Stability of Closed Elastic Curves, Proc. London Math. Soc. 79 (3) (1999) 429-450. | MR | Zbl

[10] Jurdjevic V., Hamiltonian Systems on Complex Lie Groups and Their Homogeneous Spaces, Mem. Amer. Math. Soc. 178 (838) (2005). | MR | Zbl

[11] Jurdjevic V., Geometric Control Theory, Cambridge Studies in Advanced Mathematics, vol. 51, Cambridge Univ. Press, New York, 1997. | MR | Zbl

[12] Jurdjevic V., Monroy-Perez F., Hamiltonian Systems on Lie Groups: Elastic Curves, Tops and Constrained Geodesic Problems, in: Non-Linear Geometric Control Theory and Its Applications, World Scientific Publishing Co., Singapore, 2002, pp. 3-52. | MR | Zbl

[13] Jurdjevic V., Hamiltonian Systems on Lie Groups: Kowalewski Type, Ann. Math. 150 (1999) 1-40. | MR | Zbl

[14] Langer J., Perline R., Poisson Geometry of the Filament Equation, J. Nonlinear Sci. 1 (1978) 71-93. | MR | Zbl

[15] Magri F., A Simple Model for the Integrable Hamiltonian Equation, J. Math. Phys. 19 (1978) 1156-1162. | MR | Zbl

[16] Millson J., Zombro B. A., A Kähler Structure on the Moduli Spaces of Isometric Maps of a Circle Into Euclidean Spaces, Invent. Math. 123 (1) (1996) 35-59. | MR | Zbl

[17] Shabat C., Zakharov V., Exact Theory of Two Dimensional Self-Focusing and One Dimensional Self-Modulation of Waves in Non-Linear Media, Sov. Phys. JETP 34 (1972) 62-69. | MR

[18] Sternberg S., Lectures on Differential Geometry, Prentice-Hall Inc., Englewood-Cliffs, NJ, 1964. | MR | Zbl

Cité par Sources :