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Russian Mathematical Surveys, 2017, Volume 72, Issue 1, Pages 101–178
DOI: https://doi.org/10.1070/RM9745 (Mi rm9745) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Dynamics of skew products of interval maps

L. S. Efremova

Nizhnii Novgorod State University
English version PDF (1239 kB) Citations (13) Russian version article
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DOI: https://doi.org/10.1070/RM9745
Abstract: In the study of dynamical systems in the class of skew products, the present paper involves the direction most closely connected with advances in one-dimensional dynamics. The main results obtained over the last decades on the dynamics of skew products of interval maps are surveyed. Included here are new results on the structure of the non-wandering set and the centre for $C^1$-smooth skew products of interval maps that are endomorphisms whose quotient maps have complicated dynamics. These results are used to describe the space of skew products of this type.
Bibliography: 125 titles.
Keywords: skew product of interval maps, non-wandering set, centre, depth of the centre, stability as a whole of a family of fibre maps, $\Omega$-stability, dense stability as a whole of a family of fibre maps.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.3287.2017
This research was partially supported by the Russian Ministry of Science and Education (project 1.3287.2017, target part).
Received: 11.02.2016
Revised: 14.09.2016
Bibliographic databases:
Document Type: Article
UDC: 517.987.5
MSC: Primary 37B20, 37E30; Secondary 37E05
Language: English
Original paper language: Russian
Citation: L. S. Efremova, “Dynamics of skew products of interval maps”, Russian Math. Surveys, 72:1 (2017), 101–178
Citation in format AMSBIB
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\by L.~S.~Efremova
\paper Dynamics of skew products of interval maps
\jour Russian Math. Surveys
\yr 2017
\vol 72
\issue 1
\pages 101--178
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  • https://doi.org/10.1070/RM9745
  • https://www.mathnet.ru/eng/rm/v72/i1/p107
    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:1587
    Russian version PDF:437
    English version PDF:96
    References:266
    First page:162
     
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