Geodesic
Regular components of homeomorphisms of the $n$-dimensional sphere
Sbornik. Mathematics, Tome 14 (1971) no. 1, pp. 1-14 
S. Kh. Aranson; V. S. Medvedev. Regular components of homeomorphisms of the $n$-dimensional sphere. Sbornik. Mathematics, Tome 14 (1971) no. 1, pp. 1-14. http://geodesic.mathdoc.fr/item/SM_1971_14_1_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the structure of the regular components of homeomorphisms of the $n$-dimensional sphere is studied. Results are obtained which turn out to describe the possible types of regular components, and which generalize to dimensions $n\geqslant3$ the results of Birkhoff and Smith in dimension $2$. As applications we describe the regular components of structurally stable diffeomorphisms of $S^n$ with a finite number of periodic points and the connected components of orbitally stable trajectories of a structurally stable dynamical system on $S^n$ with a finite number of closed trajectories. Bibliography: 6 titles.

[1] G. Birkhoff, P. Smith, “Structure analysis of surface transformations”, J. Math., 7 (1928), 345–379 | Zbl

[2] P. Smith, “The regular components of surface transformations”, Amer. J. Math., 52 (1930), 357–369 | DOI | MR | Zbl

[3] E. Leontovich, A. Maier, “O traektoriyakh, opredelyayuschikh kachestvennuyu strukturu razbieniya sfery na traektorii”, DAN SSSR, 14:5 (1937), 251–254 | Zbl

[4] L. V. Keldysh, Topologicheskie vlozheniya v evklidovo prostranstvo, Trudy Matem. in-ta im. V. A. Steklova, LXXXI, 1966 | MR

[5] M. Brown, “A proof of the generalized Schoenflies theorem”, Bull. Amer. Math. Soc., 66:2 (1960), 74–76 ; Matematika, 5:5 (1961), 13–15 | DOI | MR | Zbl

[6] Xu Sy-tszyan, Teoriya gomotetii, Mir, Moskva, 1964