Alexey Okunev

Email: aokunev57 [at] gmail.com

I am now a math postdoc at the University of Maryland, before that I was a postdoc at Penn State and at Loughborogh University (UK). I got my PhD at Higher School of Economics, where my advisor was Yulij Ilyashenko. For more information see my Curriculum Vitae.

Research

I work in dynamical systems. Most of my recent work is in perturbations of Hamiltonian systems, where a small perturbation of a completely integrable system can produce chaotic properties such as sensitivity to initial data and random phenomena. I also have a broad background and worked on problems involving iterated function systems, attractors, and partial and nonuniform hyperbolicity. For more information see my research statement and publications listed below.

Preprints

Publications

  • Averaging and passage through resonances in two-frequency systems near separatrices.
    Joint with A. Neishtadt.
    Communications in Mathematical Physics, 406.3 (2025), p.63
  • On phase at a resonance in slow-fast Hamiltonian systems.
    Joint with Y. Gao and A. Neishtadt.
    Regular and Chaotic Dynamics, 28.4 (2023): 585-612
  • Attractors with Non-Invariant Interior.
    Joint with S. Minkov and I. Shilin.
    Moscow Mathematical Journal, 23.4 (2023): 559-570
  • Phase change and order 2 averaging for one-frequency systems with separatrix crossing.
    Joint with A. Neishtadt.
    Nonlinearity, 35.8 (2022) 4469
  • A C1 Anosov diffeomorphism with a horseshoe that attracts almost any point.
    Joint with C. Bonatti, S. Minkov, and I. Shilin.
    Discrete & Continuous Dynamical Systems, 40.1 (2020): 441
  • Milnor Attractors of Skew Products with the Fiber a Circle.
    Journal of Dynamical and Control Systems, 23:2 (2017): pp. 421-433
  • Omega-limit sets of generic points of partially hyperbolic diffeomorphisms.
    Joint with S. Minkov.
    Functional Analysis and Its Applications, 50.1 (2016): 48-53
  • On the attractors of step skew products over the Bernoulli shift.
    Joint with I. Shilin.
    Proceedings of the Steklov Institute of Mathematics, 297 (2017): 260-280
  • Chiral tunneling through generic one-dimensional potential barriers in bilayer graphene.
    Joint with V. Kleptsyn, I. Schurov, D. Zubov, and M. I. Katsnelson.
    Phys. Rev. B, 92:16 (2016), 165407