On the attractors of step skew products over the Bernoulli shift

  title={On the attractors of step skew products over the Bernoulli shift},
  author={Alexey Okunev and I. S. Shilin},
  journal={Proceedings of the Steklov Institute of Mathematics},
  • A. OkunevI. Shilin
  • Published 6 March 2017
  • Mathematics
  • Proceedings of the Steklov Institute of Mathematics
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… 
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