|
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.
DOI:
https://doi.org/10.4213/rm9745
 Full text:
PDF file (1320 kB)
References:
PDF file
HTML file
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
\Bibitem{Efr17}
\by L.~S.~Efremova
\paper Dynamics of skew products of interval maps
\jour Uspekhi Mat. Nauk
\yr 2017
\vol 72
\issue 1(433)
\pages 107--192
\mathnet{http://mi.mathnet.ru/umn9745}
\crossref{https://doi.org/10.4213/rm9745}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3608031}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2017RuMaS..72..101E}
\elib{https://elibrary.ru/item.asp?id=28169183}
\transl
\jour Russian Math. Surveys
\yr 2017
\vol 72
\issue 1
\pages 101--178
\crossref{https://doi.org/10.1070/RM9745}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000401848400003}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85020007587}
Linking options:
http://mi.mathnet.ru/eng/umn9745https://doi.org/10.4213/rm9745 http://mi.mathnet.ru/eng/umn/v72/i1/p107
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:
-
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
-
A. V. Kochergin, “New examples of Besicovitch transitive cylindrical cascades”, Sb. Math., 209:9 (2018), 1257–1272
 -
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
|
| Number of views: |
| This page: | 892 | | Full text: | 73 | | References: | 137 | | First page: | 162 |
|
Terms of Use