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Nguyen Huynh Phan

On the topology of the space of reachable antisymmetric linear Hamiltonian systems. (Sur la topologie de l’espace des systèmes linéaires hamiltoniens anti-symétriques accessibles.) (French) Zbl 0811.70012

Ann. Inst. Fourier 44, No. 3, 967-985 (1994).
Summary: We construct canonical forms with continuation 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.

MSC:

70H05 Hamilton’s equations
55N10 Singular homology and cohomology theory
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems

Keywords:

homology group; Grassmann manifold
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\textit{Nguyen Huynh Phan}, Ann. Inst. Fourier 44, No. 3, 967--985 (1994; Zbl 0811.70012)
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