42 citations · 52 across the 11 of their papers we have counts for
11 papers
Weak mixing for area preserving flows on surfaces
Adam Kanigowski, Alexey Okunev, Rigoberto Zelada
Let be an area-preserving smooth flow on a compact, connected, orientable surface with at least one but finitely many fixed points. Assume that is anal…
Thick Arnold tongues
Mark Levi, Alexey Okunev
We introduce and study a physically motivated problem that exhibits interesting and perhaps unexpected mathematical features. A cellular flow is a two-dimensional Hamiltonian flow…
Attractors with non-invariant interior
Stanislav Minkov, Alexey Okunev, Ivan Shilin
We construct an open set of endomorphisms of an arbitrary two-dimensional manifold which have attractors and non-wandering sets with non-invariant interior. This is a notable contr…
On phase at a resonance in slow-fast Hamiltonian systems
Yuyang Gao, Anatoly Neishtadt, Alexey Okunev
We consider a slow-fast Hamiltonian system with one fast angular variable (a fast phase) whose frequency vanishes on some surface in the space of slow variables (a resonant surface…
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…
Averaging and passage through resonances in two-frequency systems near separatrices
Anatoly Neishtadt, Alexey Okunev
The averaging method is a classical powerful tool in perturbation theory of dynamical systems. There are two major obstacles to applying the averaging method, resonances and separa…
On the phase change for perturbations of Hamiltonian systems with separatrix crossing
Anatoly Neishtadt, Alexey Okunev
We study the evolution of angular variable (phase) for general (not necessarily Hamiltonian) perturbations of Hamiltonian systems with one degree of freedom near separatrices of th…
Classification of generic semigroup actions of circle diffeomorphisms
Victor Kleptsyn, Yury Kudryashov, Alexey Okunev
We study topological properties of semi-group actions on the circle by orientation-preserving homeomorhisms. We prove that a generic action either possesses a forward-invariant int…
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…
Milnor Attractors of Skew Products with the Fiber a Circle
Alexey Okunev
We prove that for a generic skew product with circle fiber over an Anosov diffeomorphism the Milnor attractor (also called the likely limit set) coincides with the statistical attr…
Chiral tunneling through generic one-dimensional potential barriers in bilayer graphene
V. Kleptsyn, A. Okunev, I. Schurov +2
We study tunneling of charge carriers in single- and bilayer graphene. We propose an explanation for non-zero "magic angles" with 100% transmission for the case of symmetric potent…