Geodesic
Absence of $C^1$-$\Omega$-explosion in the space of smooth simplest skew products
Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 4, Tome 48 (2013), pp. 36-50

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We give a detailed proof of absence of a $C^1$-$\Omega$-explosion in the space of $C^1$-regular simplest skew products of mappings of an interval (i.e., skew products of mappings of an interval with a closed set of periodic points). We study the influence of $C^1$-perturbations (of the class of skew products) to the set of periods of the periodic points of $C^1$-regular simplest skew products, and describe the peculiarities of period doubling bifurcations of the periodic points. 
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     author = {L. S. Efremova},
     title = {Absence of $C^1$-$\Omega$-explosion in the space of smooth simplest skew products},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {36--50},
     publisher = {mathdoc},
     volume = {48},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2013_48_a2/}
}
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L. S. Efremova. Absence of $C^1$-$\Omega$-explosion in the space of smooth simplest skew products. Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 4, Tome 48 (2013), pp. 36-50. http://geodesic.mathdoc.fr/item/CMFD_2013_48_a2/