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 CMFD, 2013, Volume 48, Pages 36–50 (Mi cmfd237)

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

L. S. Efremova

Lobachevski Nizhni Novgorod State University, Differential Equations and Mathematical Analysis Department, Nizhni Novgorod, Russia

Abstract: 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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English version:
Journal of Mathematical Sciences, 2014, 202:6, 794–808

UDC: 517.987.5

Citation: L. S. Efremova, “Absence of $C^1$-$\Omega$-explosion in the space of smooth simplest skew products”, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 4, CMFD, 48, PFUR, M., 2013, 36–50; Journal of Mathematical Sciences, 202:6 (2014), 794–808

Citation in format AMSBIB
\Bibitem{Efr13} \by L.~S.~Efremova \paper Absence of $C^1$-$\Omega$-explosion in the space of smooth simplest skew products \inbook Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14--21, 2011). Part~4 \serial CMFD \yr 2013 \vol 48 \pages 36--50 \publ PFUR \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd237} \transl \jour Journal of Mathematical Sciences \yr 2014 \vol 202 \issue 6 \pages 794--808 \crossref{https://doi.org/10.1007/s10958-014-2077-7} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84919935393} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. L. S. Efremova, V. Zh. Sakbaev, “Notion of blowup of the solution set of differential equations and averaging of random semigroups”, Theoret. and Math. Phys., 185:2 (2015), 1582–1598
2. L. S. Efremova, “Dynamics of skew products of interval maps”, Russian Math. Surveys, 72:1 (2017), 101–178
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