Geodesic
On the structure of the set of invariant subspaces for a linear mapping
Trudy Instituta matematiki, Tome 14 (2006) no. 2, pp. 11-19 
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/
@article{TIMB_2006_14_2_a1,
     author = {A. B. Antonevich and C. Doli\'canin and S. Re\v{s}i\'c},
     title = {On the structure of the set of invariant subspaces for a linear mapping},
     journal = {Trudy Instituta matematiki},
     pages = {11--19},
     year = {2006},
     volume = {14},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2006_14_2_a1/}
}
TY  - JOUR
AU  - A. B. Antonevich
AU  - C. Dolićanin
AU  - S. Rešić
TI  - On the structure of the set of invariant subspaces for a linear mapping
JO  - Trudy Instituta matematiki
PY  - 2006
SP  - 11
EP  - 19
VL  - 14
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TIMB_2006_14_2_a1/
LA  - ru
ID  - TIMB_2006_14_2_a1
ER  - 
%0 Journal Article
%A A. B. Antonevich
%A C. Dolićanin
%A S. Rešić
%T On the structure of the set of invariant subspaces for a linear mapping
%J Trudy Instituta matematiki
%D 2006
%P 11-19
%V 14
%N 2
%U http://geodesic.mathdoc.fr/item/TIMB_2006_14_2_a1/
%G ru
%F TIMB_2006_14_2_a1

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[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