Sur la topologie de l'espace des systèmes linéaires hamiltoniens anti symétriques accessibles

Phan Nguyen Huynh

Annales de l'institut Fourier (1994)

  • Volume: 44, Issue: 3, page 967-985
  • ISSN: 0373-0956

Abstract

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

How to cite

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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 44.3 (1994): 967-985. <http://eudml.org/doc/75086>.

@article{PhanNguyenHuynh1994,
abstract = {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.},
author = {Phan Nguyen Huynh},
journal = {Annales de l'institut Fourier},
keywords = {homology group; Grassmann manifold},
language = {fre},
number = {3},
pages = {967-985},
publisher = {Association des Annales de l'Institut Fourier},
title = {Sur la topologie de l'espace des systèmes linéaires hamiltoniens anti symétriques accessibles},
url = {http://eudml.org/doc/75086},
volume = {44},
year = {1994},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 44
IS - 3
SP - 967
EP - 985
AB - 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.
LA - fre
KW - homology group; Grassmann manifold
UR - http://eudml.org/doc/75086
ER -

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