4 papers
Attractors with Non-Invariant Interior and Pinheiro's Theorem A
Stanislav Minkov, Alexey Okunev, Ivan Shilin
This is a provisional version of an article, intended to be devoted to properties of attractor's intertior for smooth maps (not diffeomorphisms). We were originally motivated for t…
Attractors of direct products
Stanislav Minkov, Ivan Shilin
For Milnor, statistical, and minimal attractors, we construct examples of smooth flows on for which the attractor of the Cartesian square of is smaller than the Carte…
On the attractors of step skew products over the Bernoulli shift
Alexey Okunev, Ivan Shilin
The statistical and Milnor attractors of step skew products over the Bernoulli shift are studied. For the case of the fiber a circle we prove that for a topologically generic step…
Locally topologically generic diffeomorphisms with Lyapunov unstable Milnor attractors
Ivan Shilin
We prove that for every smooth compact manifold and any , whenever there is an open domain in exhibiting a persistent homoclinic tangency related…