Lagrange Intersections in a Symplectic Space
Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 4, pp. 64-70.

Voir la notice de l'article provenant de la source Math-Net.Ru

The two-dimensional torus $|z_1|=|z_2|=1$ in the symplectic space $\mathbb{C}^2$ and the image of it under a linear symplectomorphism have at least eight common points (counted according to their multiplicities). We also prove a many-dimensional version of this theorem of symplectic linear algebra.
@article{FAA_2000_34_4_a4,
     author = {P. E. Pushkar'},
     title = {Lagrange {Intersections} in a {Symplectic} {Space}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {64--70},
     publisher = {mathdoc},
     volume = {34},
     number = {4},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2000_34_4_a4/}
}
TY  - JOUR
AU  - P. E. Pushkar'
TI  - Lagrange Intersections in a Symplectic Space
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2000
SP  - 64
EP  - 70
VL  - 34
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2000_34_4_a4/
LA  - ru
ID  - FAA_2000_34_4_a4
ER  - 
%0 Journal Article
%A P. E. Pushkar'
%T Lagrange Intersections in a Symplectic Space
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2000
%P 64-70
%V 34
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2000_34_4_a4/
%G ru
%F FAA_2000_34_4_a4
P. E. Pushkar'. Lagrange Intersections in a Symplectic Space. Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 4, pp. 64-70. http://geodesic.mathdoc.fr/item/FAA_2000_34_4_a4/

[1] Arnold V. I., “O kharakteristicheskom klasse, vkhodyaschem v uslovie kvantovaniya”, Funkts. analiz i ego pril., 1:1 (1967), 1–14 | MR

[2] Arnold V. I., “Teoremy Shturma i simplekticheskaya geometriya”, Funkts. analiz i ego pril., 19:4 (1985), 1–10 | DOI | MR

[3] Arnold V. I., “Mody i kvazimody”, Funkts. analiz i ego pril., 6:2 (1972), 12–20 | MR

[4] Lerman L. M., “O gamiltonovykh sistemakh s petlei separatrisy sedlo-tsentra”, Metody kachestvennoi teorii differentsialnykh uravnenii, Mezhvuz. sb. nauchn. trudov pod red. N. A. Leontovich-Andronovoi, Gorkovskii gosuniversitet, Gorkii, 1987, 89–103 | MR | Zbl

[5] Koltsova O. Yu., Lerman L. M., “Transverse Poincaré homoclinic orbits in a $2N$-dimensional Hamiltonian system close to the system with a loop to a saddle-center”, Int. J. Bifurcation and Chaos, 6:6 (1996), 991–1006 | DOI | MR | Zbl

[6] Koltsova O. Yu., Lerman L. M., “Transversalnye gomoklinicheskie traektorii Puankare okolo petli sedlo-tsentra v $2N$-mernoi gamiltonovoi sisteme”, Dokl. RAN, 359:4 (1998), 448–451 | MR

[7] Floer A., “Morse theory for Lagrangian intersections”, J. Diff. Geom., 28 (1988), 513–547 | MR | Zbl

[8] Floer A., “Witten's complex and infinite dimensional Morse theory”, J. Diff. Geom., 30 (1989), 207–221 | MR | Zbl

[9] Givental A. B., “Nonlinear generalization of the Maslov index”, Adv. Soviet Math., 1 (1990), 71–103 | MR | Zbl