Geodesic
Certain Properties of Skew Products over a~Horseshoe and a~Solenoid
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems, automata, and infinite groups, Tome 231 (2000), pp. 96-118.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TM_2000_231_a3,
     author = {A. S. Gorodetski and Yu. S. Ilyashenko},
     title = {Certain {Properties} of {Skew} {Products} over {a~Horseshoe} and {a~Solenoid}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {96--118},
     publisher = {mathdoc},
     volume = {231},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2000_231_a3/}
}
TY  - JOUR
AU  - A. S. Gorodetski
AU  - Yu. S. Ilyashenko
TI  - Certain Properties of Skew Products over a~Horseshoe and a~Solenoid
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2000
SP  - 96
EP  - 118
VL  - 231
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2000_231_a3/
LA  - ru
ID  - TM_2000_231_a3
ER  - 
%0 Journal Article
%A A. S. Gorodetski
%A Yu. S. Ilyashenko
%T Certain Properties of Skew Products over a~Horseshoe and a~Solenoid
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2000
%P 96-118
%V 231
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2000_231_a3/
%G ru
%F TM_2000_231_a3
A. S. Gorodetski; Yu. S. Ilyashenko. Certain Properties of Skew Products over a~Horseshoe and a~Solenoid. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems, automata, and infinite groups, Tome 231 (2000), pp. 96-118. http://geodesic.mathdoc.fr/item/TM_2000_231_a3/

[1] Gorodetskii A. S., Ilyashenko Yu. S., “Nekotorye novye grubye svoistva invariantnykh mnozhestv i attraktorov dinamicheskikh sistem”, Funkts. analiz i ego pril., 33:2 (1999), 16–30 | MR

[2] Hirsh M., Pugh C., Shub M., Invariant manifolds, Springer-Verl., N. Y. etc., 1977, Lect. Notes Math., v. 583 | MR

[3] Kostelich E. J., Kan Ittai, Grebogi C., Ott E., Yorke J., “Unstable dimention variability: A source of nonhyperbolicity chaotic systems”, Physica D, 109 (1997), 81–90 | DOI | MR | Zbl

[4] Bonatti C., Diaz L. J., “Persistent nonhyperbolic transitive diffeomorphisms”, Ann. Math., ser. 2, 143:2 (1996), 357–396 | DOI | MR | Zbl