Absence of $C^1$-$\Omega$-explosion in the space of smooth simplest skew products

L. S. Efremova

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.

Résumé

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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