On the structure of the set of invariant subspaces for a linear mapping
Trudy Instituta matematiki, Tome 14 (2006) no. 2, pp. 11-19.

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For a linear transformation of a finite dimensional space the topological structure of the set of its invariant subspaces is considered. The number of connected components of this set is found. It is shown that every component has a structure of a fibre bundle.
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A. B. Antonevich; C. Dolićanin; S. Rešić. On the structure of the set of invariant subspaces for a linear mapping. Trudy Instituta matematiki, Tome 14 (2006) no. 2, pp. 11-19. http://geodesic.mathdoc.fr/item/TIMB_2006_14_2_a1/

[1] Lankaster P., Teoriya matrits, M., 1978 | MR

[2] Godunov B., Zabreiko P., “Geometric characteristics for convergence and asymptotics of successive approximations of equations with smooth operators”, Studia Math., 116 (1995), 225–238 | MR | Zbl

[3] Antonevich A., Buraczewski A., “Dynamics of linear mapping and invariant measures on sphere”, Demonstratio Math., 29:4 (1996), 817–824 | MR

[4] Antonevich A.B., Dolichanin Ch., Nikolich G., “Dinamika lineinogo otobrazheniya na mnogoobrazii Grassmana. Sluchai Perrona”, Trudy In-ta matematiki NAN Belarusi. Minsk, 9 (2001), 20–23

[5] Antonevich A., Dolichanin Ch., Nicolich G., “Dynamics of a Linear Mapping on the Grassman Manifold. Case of different Eigenvalues”, Spestral and Evolution Problems, 11, Simferopol, 2001, 70–72 | MR

[6] Gantmakher F.R., Teoriya matrits, M., 1967

[7] Gohberg I., Lancaster P., Rodman L., Invariant subspace of matrices with applications, Willey Sons, New York; Chichester; Toronto; Singapore, 1986 | MR | Zbl

[8] Khyuzmoller D., Rassloennye prostranstva, M., 1970