Geodesic
On the attractors of step skew products over the Bernoulli shift
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Order and chaos in dynamical systems, Tome 297 (2017), pp. 260-280

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We study the statistical and Milnor attractors of step skew products over the Bernoulli shift. In the case when the fiber is a circle, we prove that for a topologically generic step skew product the statistical and Milnor attractors coincide and are Lyapunov stable. To this end we study some properties of the projection of the attractor onto the fiber, which might be of independent interest. In the case when the fiber is a segment, we give a description of the Milnor attractor as the closure of the union of graphs of finitely many almost everywhere defined functions from the base of the skew product to the fiber. 
@article{TM_2017_297_a13,
     author = {A. V. Okunev and I. S. Shilin},
     title = {On the attractors of step skew products over the {Bernoulli} shift},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {260--280},
     publisher = {mathdoc},
     volume = {297},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2017_297_a13/}
}
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A. V. Okunev; I. S. Shilin. On the attractors of step skew products over the Bernoulli shift. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Order and chaos in dynamical systems, Tome 297 (2017), pp. 260-280. http://geodesic.mathdoc.fr/item/TM_2017_297_a13/