Geodesic
On smooth mappings of the circle into itself
Sbornik. Mathematics, Tome 14 (1971) no. 2, pp. 161-185

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In this article is constructed the set $\mathfrak M=\mathfrak M_1\cup\mathfrak M_2$, open and everywhere dense in $C^1(S^1,S^1)$, of $\Omega$-stable mappings. $\Omega(f)$ is totally disconnected and $f/\Omega(f)$ is topologically conjugate to the topological Markov chain with a finite number of states; for $f\in\mathfrak M_2$ we have $\Omega(f)=S^1$ and $f/S^1$ topologically conjugate to $z^n/S^1$. For $f\in\mathfrak M$ there exists a hyperbolic structure onЁ$\Omega(f)$. Figures: 1 Bibliography: 9 titles. 
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     author = {M. V. Jakobson},
     title = {On smooth mappings of the circle into itself},
     journal = {Sbornik. Mathematics},
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     number = {2},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_14_2_a0/}
}
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M. V. Jakobson. On smooth mappings of the circle into itself. Sbornik. Mathematics, Tome 14 (1971) no. 2, pp. 161-185. http://geodesic.mathdoc.fr/item/SM_1971_14_2_a0/