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JOURNALS // Teoreticheskaya i Matematicheskaya Fizika // Archive

TMF, 2010 Volume 164, Number 3, Pages 447–454 (Mi tmf6556)

This article is cited in 9 papers

Space of $C^1$-smooth skew products of maps of an interval

L. S. Efremova

Lobachevsky Nizhnii Novgorod State University (Research University), Nizhnii Novgorod, Russia

Abstract: 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, quotient map, $\Omega$-function, suitable function.

DOI: 10.4213/tmf6556


 English version:
Theoretical and Mathematical Physics, 2010, 164:3, 1208–1214

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© Steklov Math. Inst. of RAS, 2025