Geodesic
Space of $C^1$-smooth skew products of maps of an~interval
Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 3, pp. 447-454

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Using the notions of an $\Omega$-function and of functions suitable for an $\Omega$-function, we show that the space of $C^1$-smooth skew products of maps of an interval such that the quotient map of each is $\Omega$-stable in the space of $C^1$-smooth maps of a closed interval into itself and has a type $\succ2^{\infty}$ (i.e., contains a periodic orbit with the period not equal to a power of $2$) can be represented as a union of four nonempty pairwise nonintersecting subspaces. We give examples of maps belonging to each of the identified subspaces.
Keywords: skew product, $\Omega$-function, suitable function.
Mots-clés : quotient map 
@article{TMF_2010_164_3_a14,
     author = {L. S. Efremova},
     title = {Space of $C^1$-smooth skew products of maps of an~interval},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {447--454},
     publisher = {mathdoc},
     volume = {164},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_164_3_a14/}
}
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L. S. Efremova. Space of $C^1$-smooth skew products of maps of an~interval. Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 3, pp. 447-454. http://geodesic.mathdoc.fr/item/TMF_2010_164_3_a14/