Sur la topologie de l'espace des systèmes linéaires hamiltoniens anti symétriques accessibles
Annales de l'Institut Fourier, Volume 44 (1994) no. 3, pp. 967-985.

In this paper we construct canonical forms with continue on the strata of the stratification on the space of reachable antisymmetric hamiltonian linear systems HA n,m,p . We prove that the homology group of HA n,m,p is isomorphic to those of the Grassmann manifold. Then we prove that HA n,m,p is homotopically equivalent to the space of reachable linear systems.

Dans cet article nous donnons les formes normales des sytèmes linéaires hamiltoniens antisymétriques accessibles HA n,m,p . Nous construisons une stratification et une décomposition cellulaire analytique de HA n,m,p , puis nous prouvons que son groupe d’homotopie est isomorphe à celui d’une grassmanienne. Ensuite, nous démontrons que HA n,m,p 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.

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Phan Nguyen Huynh. Sur la topologie de l'espace des systèmes linéaires hamiltoniens anti symétriques accessibles. Annales de l'Institut Fourier, Volume 44 (1994) no. 3, pp. 967-985. doi : 10.5802/aif.1422. http://archive.numdam.org/articles/10.5802/aif.1422/

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