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Tr. Mat. Inst. Steklova, 2000, Volume 231, Pages 96–118 (Mi tm513)  

This article is cited in 34 scientific papers (total in 34 papers)

Certain Properties of Skew Products over a Horseshoe and a Solenoid

A. S. Gorodetski, Yu. S. Ilyashenko


Abstract: The skew products are investigated over the Bernoulli shift and the Smale–Williams solenoid with a fiber $S^1$. It is assumed that the mapping in the fiber Hölder continuously depends on a point in the base (it is these skew products that arise in the study of partially hyperbolic sets). It is proved that, in the space of skew products with this property, there exists an open domain such that the mappings from this domain have dense sets of periodic orbits that are attracting and repelling along the fiber, as well as the dense orbits with the zero (along the fiber) Lyapunov exponent.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2000, 231, 90–112

Bibliographic databases:

UDC: 517.938
Received in February 2000

Citation: A. S. Gorodetski, Yu. S. Ilyashenko, “Certain Properties of Skew Products over a Horseshoe and a Solenoid”, Dynamical systems, automata, and infinite groups, Collected papers, Tr. Mat. Inst. Steklova, 231, Nauka, MAIK Nauka/Inteperiodika, M., 2000, 96–118; Proc. Steklov Inst. Math., 231 (2000), 90–112

Citation in format AMSBIB
\Bibitem{GorIly00}
\by A.~S.~Gorodetski, Yu.~S.~Ilyashenko
\paper Certain Properties of Skew Products over a~Horseshoe and a~Solenoid
\inbook Dynamical systems, automata, and infinite groups
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2000
\vol 231
\pages 96--118
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm513}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1841753}
\zmath{https://zbmath.org/?q=an:1002.37017}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2000
\vol 231
\pages 90--112


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