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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2000, Volume 231, Pages 96–118
(Mi tm513)
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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.
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, Trudy Mat. Inst. Steklova, 231, Nauka, MAIK «Nauka/Inteperiodika», M., 2000, 96–118; Proc. Steklov Inst. Math., 231 (2000), 90–112
Linking options:
https://www.mathnet.ru/eng/tm513 https://www.mathnet.ru/eng/tm/v231/p96
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