Abstract
We give a detailed proof of absence of a C 1- Ω-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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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 48, Proceedings of the Sixth International Conference on Differential and Functional Differential Equations and International Workshop “Spatio-Temporal Dynamical Systems” (Moscow, Russia, 14–21 August, 2011). Part 4, 2013.
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Efremova, L. Absence of C 1- Ω-Explosion in the Space of Smooth Simplest Skew Products. J Math Sci 202, 794–808 (2014). https://doi.org/10.1007/s10958-014-2077-7
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DOI: https://doi.org/10.1007/s10958-014-2077-7