Department of Mathematics
The Ohio State University
- E-mail gogolyev.1_located_at_osu_dot_edu
- Office MW 652
My research interest is in dynamics and related areas of topology and geometry.
Recent papers and preprints
- Smooth rigidity for very non-algebraic Anosov diffeomorphisms of codimension one (joint with Federico Rodriguez Hertz) and earlier version which includes only the basic 3-dimensional case.
- Riemannian Anosov extension and applications (joint with Alena Erchenko and Dong Chen).
- Abelian Livshits theorems and geometric applications (joint with Federico Rodriguez Hertz) to appear in Anatole Katok CUP memorial volume.
- Surgery for partially hyperbolic dynamical systems II. Blow-up of a complex curve (joint with Federico Rodriguez Hertz) Mathematische Zeitschrift, 298 (2021), no. 3-4, 1793–1811.
- Smooth rigidity for very non-algebraic expanding maps (joint with Federico Rodriguez Hertz) to appear in Journal of European Math Society.
- Centralizers of partially hyperbolic diffeomorphisms in dimension 3 (joint with Thomas Barthelmé) Discrete Continuous Dynamical Systems, series A, 41 (2021), no. 9, 4477–4484.
- Center foliation rigidity for partially hyperbolic toral diffeomorphisms
(joint Boris Kalinin and Victoria Sadovskaya).
- Local rigidity of Lyapunov spectrum for toral automorphisms (joint with Boris Kalinin and Victoria Sadovskaya) Israel Journal of Mathematics, 238 (2020), no. 1, 389-403.
- Anomalous Anosov flows revisited (joint with Thomas Barthelmé, Christian Bonatti and Federico Rodriguez Hertz) Proceedings of London Math Society, vol. 122 (2021), issue 1, 93-117.
- A numerical study of Gibbs u-measures for partially hyperbolic diffeomorphisms on T3 (joint with Aleksey Kolmogorov and Itai Maimon) Experimental Mathematics, 28 (2019), no. 3, 271–283. For a version with high quality images click here, 17MB file .
- Anomalous partially hyperbolic diffeomorphisms III: abundance and incoherence (joint with Christian Bonatti, Andy Hammerlindl and Rafael Potrie) Geometry & Topology, 24-4 (2020), 1751-1790.
- A note on self orbit equivalences of Anosov flows and bundles with fiberwise Anosov flows (joint with Thomas Barthelmé) Mathematical Research Letters, 26 (2019), no. 3, 711-728.
- Surgery for partially hyperbolic dynamical systems I.
Blow-ups of invariant submanifolds Geometry & Topology, 22 (2018), no. 4, 2219–2252.
Students: Danyu Zhang, James Marshall Reber, Thomas Aloysius O'Hare
Fall 2021: Dynamical Systems, math 4556
Fall 2020: Differentiable Manifolds,
Honors Linear Algebra and Differential Equations, math 5520H
Spring 2020: Introduction to Real Analysis I, math 4547
Fall 2019: Differentiable Manifolds
Fall 2018: Algebraic Topology I
Spring 2018: ODEs, math 2255
Fall 2017: Dynamical Systems, math 4556
Travel plans and visitors
Dynamics on your screen, August 3-6, 2020; A Hyperbolic Day Online , February 4th, 2021
My old picture with Lyapunov, Odessa 2006.
My math bookmarks: