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
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.
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.
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Russian Mathematical Surveys, 2017, 72:1, 101–178
MSC: Primary 37B20, 37E30; Secondary 37E05
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
\paper Dynamics of skew products of interval maps
\jour Uspekhi Mat. Nauk
\jour Russian Math. Surveys
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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
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