Dans cet article nous donnons les formes normales des sytèmes linéaires hamiltoniens antisymétriques accessibles . Nous construisons une stratification et une décomposition cellulaire analytique de , puis nous prouvons que son groupe d’homotopie est isomorphe à celui d’une grassmanienne. Ensuite, nous démontrons que est homotopiquement équivalent à l’espace des systèmes linéaires accessibles. En appliquant ces résultats topologiques, on peut prouver qu’il n’existe pas de paramétrisation continue de tous les systèmes hamiltoniens antisymétriques accessibles si la dimension de l’espace d’entrée est plus grande que 1. En utilisant des travaux de M. Guest et U. Helmke, on peut ainsi donner une démonstration du théorème de périodicité de Bott.
In this paper we construct canonical forms with continue on the strata of the stratification on the space of reachable antisymmetric hamiltonian linear systems . We prove that the homology group of is isomorphic to those of the Grassmann manifold. Then we prove that is homotopically equivalent to the space of reachable linear systems.
@article{AIF_1994__44_3_967_0,
author = {Phan Nguyen Huynh},
title = {Sur la topologie de l'espace des syst\`emes lin\'eaires hamiltoniens anti sym\'etriques accessibles},
journal = {Annales de l'Institut Fourier},
pages = {967--985},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {44},
number = {3},
year = {1994},
doi = {10.5802/aif.1422},
zbl = {0811.70012},
language = {fr},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1422/}
}
TY - JOUR AU - Phan Nguyen Huynh TI - Sur la topologie de l'espace des systèmes linéaires hamiltoniens anti symétriques accessibles JO - Annales de l'Institut Fourier PY - 1994 SP - 967 EP - 985 VL - 44 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1422/ DO - 10.5802/aif.1422 LA - fr ID - AIF_1994__44_3_967_0 ER -
%0 Journal Article %A Phan Nguyen Huynh %T Sur la topologie de l'espace des systèmes linéaires hamiltoniens anti symétriques accessibles %J Annales de l'Institut Fourier %D 1994 %P 967-985 %V 44 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1422/ %R 10.5802/aif.1422 %G fr %F AIF_1994__44_3_967_0
Phan Nguyen Huynh. Sur la topologie de l'espace des systèmes linéaires hamiltoniens anti symétriques accessibles. Annales de l'Institut Fourier, Tome 44 (1994) no. 3, pp. 967-985. doi : 10.5802/aif.1422. https://aif.centre-mersenne.org/articles/10.5802/aif.1422/
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