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Uspekhi Mat. Nauk, 2017, Volume 72, Issue 1(433), Pages 107–192 (Mi umn9745)  

This article is cited in 3 scientific papers (total in 3 papers)

Dynamics of skew products of interval maps

L. S. Efremova

Nizhnii Novgorod State University

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).


DOI: https://doi.org/10.4213/rm9745

Full text: PDF file (1320 kB)
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English version:
Russian Mathematical Surveys, 2017, 72:1, 101–178

Bibliographic databases:

UDC: 517.987.5
MSC: Primary 37B20, 37E30; Secondary 37E05
Received: 11.02.2016
Revised: 14.09.2016

Citation: L. S. Efremova, “Dynamics of skew products of interval maps”, Uspekhi Mat. Nauk, 72:1(433) (2017), 107–192; Russian Math. Surveys, 72:1 (2017), 101–178

Citation in format AMSBIB
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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, “The trace map and integrability of the multifunctions”, European Conference - Workshop Nonlinear Maps and Applications, Journal of Physics Conference Series, 990, IOP Publ. Ltd, 2018, 012003  crossref  mathscinet  isi  scopus
    2. A. V. Kochergin, “New examples of Besicovitch transitive cylindrical cascades”, Sb. Math., 209:9 (2018), 1257–1272  mathnet  crossref  crossref  adsnasa  isi  elib
    3. L. S. Efremova, A. D. Grekhneva, V. Zh. Sakbaev, “Phase flows generated by Cauchy problem for nonlinear Schrödinger equation and dynamical mappings of quantum states”, Lobachevskii J. Math., 40:10 (2019), 1455–1469  crossref  mathscinet  zmath  isi
  • Успехи математических наук Russian Mathematical Surveys
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