Sergey Tikhomirov


Associate Professor of Saint-Petersburg State University
Special program "Mathematics and Theoretical Computer Science"
14th lane 29B, Vasilievsky Island,
St. Petersburg, 199178, Russia
Tel: +79213387396

Habilitation degree, University of Leipzig, 2016
Thesis: "Quantitative properties of infinite and finite pseudotrajectories". Chief of Committee: S. Luckhaus
Habilitation degree, Institute for Information Transmission Problems, 2016
Thesis: "Dynamical Systems with various shadowing properties". Chief of Committee: Ya. G. Sinai
Ph.D. degree in mathematics
, Saint-Petersburg State University, 2009
Thesis title: "Shadowing of pseudotrajectories in smooth flows". Advisor: Sergei Yurievich Pilyugin
Master degree in mathematics, Saint-Petersburg State University, 2000-2005


Cites in bibliographic databases: Mathscinet, Scholar


Research interests: Dynamical Systems. Seminar "Dinamika"
  • Quantum Computing
  • Lattice Dynamical Systems
    • Pinning/depinning
  • Hysteresis (Project A4 of the DFG Collaborative Research Center 910 on Control of self-organizing nonlinear systems)
    • Free boundary problem
    • Pattern Formation
  • Shadowing, Hyperbolicity, Partial hyperbolicity
    • Skew products
    • Actions of nonabelian groups
    • Nonuniformly hyperbolic systems
  • Numerical Simulations

Teaching:
2017: Dynamical Systems (динамические системы) Link
2017: Geometry and topology (геометрия и топология) Link
Past:
2016: Differential equations (дифференциальные уравнения) Link
2016: Geometry and topology (геометрия и топология) Link
2016: Differentiable Dynamical Systems. Introduction to chaos. Link
2015: Differentiable Dynamical Systems I. Link
2015: Smooth dynamical systems. Link
2012, 2013: Differential equations I, II. Link I, Link II
2011: On shadowing properties of differentiable dynamics. Link
2009: Shadowing and structural stability. 
Link
  1. Tikhomitrov S. (with Gurevich P.) Rattling in spatially discrete diffusion equations with hysteresis [arXiv] 
    accepted by 
    Multiscale Modeling and Simulation
  2. Tikhomirov S. (with T. Fisher, T. Petty) Nonlocally maximal and premaximal hyperbolic sets [arXiv]
    accepted by Communications in Contemporary Mathematics
  3. Tikhomirov S. On absolute nonshadowability of transitive maps [arXiv]
    Differential Equations and Control Processes (2016), N3 57-65

  4. Tikhomirov S. (with Curran M., Gurevich P.) Recent Advances in reaction-diffusion equations with non-ideal relay [arXiv]
    Control of Self-Organizing Nonlinear Systems
    (2016), Understanding Complex Systems, pp. 211-234, Springer
  5. Tikhomirov S. (with Gan S., Li M.) Oriented shadowing property and $Ω$-stability for vector fields [arXiv]
    Journal of Dynamics and Differential Equations
    28 (2016), 225-237
  6. Tikhomirov S. An example of a vector field with the oriented shadwoing property [arXiv]
    Journal of Dynamics and Control Systems. 21 (2015), no. 4, 643-654
  7. Tikhomirov S. Shadowing in linear skew products [arXiv]
    Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. 432 (2015) 261-273
  8. Tikhomirov S. Holder Shadowing on Finite Intervals  [arXiv]
    Ergodic Theory and Dynamical Systems, 35 (2015), no. 06, pp. 2000-2016 
  9. Tikhomirov S. (with A. Osipov) Shadowing in actions of finitely-generated groups [arXiv]
    Dyn. Syst. 29 (2014), no. 3, 337–351.
  10. Tikhomirov S. (with Gurevich P.) Systems of reaction-diffusion equations with spatially distributed hysteresis [arXiv]
    Mathematica Bohemica 139 (2014), No. 2, pp. 239-257
  11. Tikhomirov S. (with Kryzhevich S.) Partial hyperbolicity and central shadowing [pdfarXiv]
    DCDS - A 33 (2013), 2901-2909 
  12. Tikhomirov S. (with Gurevich P., Shamin R.) Reaction-diffusion equations with spatially distributed hysteresis [arXiv]
    SIAM J. Math. Anal. 45 (2013), no. 3, 1328–1355.
  13. Tikhomirov S. (with Gurevich P.) Uniqueness of transverse solutions for reaction-diffusion equations with spatially distributed hysteresis [arXiv]
    Nonlinear Analysis 75 (2012) 6610-6619
  14. Tikhomirov S. (with Pilyugin S.Yu., Palmer K.J.) Lipschitz shadowing for Flows [pdfarXiv
  15. J. Differential Equations 252 (20121723-1747
  16. Tikhomirov S. (with Gurevich P.) Symmetric periodic solutions of parabolic problems with hysteresis. [pdfarXiv
    Journal of Dynamics and Differential Equations 23 (2011) 923-960
  17. Tikhomirov S. (with Pilyugin S. Yu.) On Lipschitz Shadowing and structural stability [pdf, arXiv]
    Nonlinearity 23 (2010) 2509–2515

  18. Tikhomirov S. (with Pilyugin S. Yu., Osipov A. V.) Periodic Shadowing and $\Omega$-stability [pdf, arXiv]
    Regul. Chaotic Dyn. 15 (2010), no. 2-3, 404–417.
  19. Tikhomirov S. (with Pilyugin S. Yu.) Vector fields with the oriented shadowing property [pdf, arXiv]
    J. Differential Equations 248 (2010), no. 6, 1345–1375
  20. Tikhomirov S. (with Pilyugin S. Yu.) Sets of vector fields with various shadowing properties of pseudotrajectories [pdf, arXiv]
    Doklady Mathematics. (2008), Vol. 78. N. 2. p. 669-670.
  21. Tikhomirov S. Interiors of sets of vector fields corresponding to some classes of reparametrizations [pdf, arXiv]
    Vestnik Saint-Peterburg University. Mathematics. (2008), N.4 p. 90-97
  22. Tikhomirov S. A method for investigation of a neighborhood of a nontransverse homoclinic point of a two-dimensional diffeomorphism [pdf, in Russian]
    Diff. Equat. and Control Processes. (2006), N1, p. 48-77.
  23. Tikhomirov S. (with Pilyugin S. Yu.) Shadowing in actions of some abelian groups [pdf]
    Fund. Math. (2003) Vol. 179. pp. 83-96.

Works in Progress
  • Tikhomirov S. (with Gurevich P.) Spatially discrete reaction-diffusion equations with discontinuous hysteresis [arXiv]
  • Tikhomitrov S. (with Scheel A.) Depinning asymptotics in ergodic media [arXiv]

Links