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Nataliia Goncharuk

H.C. Wang Assistant Professor

Malott Hall, Room 587
ng432@cornell.edu

Educational Background

Ph.D. (2016) Institute for Information Transmission Problems, Moscow

Keywords

Dynamical systems and differential equations

Departments/Programs

  • Mathematics

Research

I am currently interested in global bifurcations of planar vector fields. My previous research concerns:

circle dynamics and its relations to one-dimentional complex dynamics;
geometry of polynomial foliations in С^2.

Courses

Publications

Complex rotation numbers and bubbles:

  • Rotation numbers and moduli of elliptic curves, Functional Analysis and Its Applications, 46:1, (2012), pp. 11–25. (translated from Russian)
  • X.Buff, N. Goncharuk, "Complex rotation numbers", Journal of Modern Dynamics, Volume 9 (2015), pp. 169-190.
  • “Complex rotation numbers: bubbles and their intersections” (arXiv:1708.01077), accepted to Analysis and PDE.

  • Self-similarity of bubbles, arXiv:1805.04769.

Polynomial foliations in C^2:

  • N. Goncharuk, Yu. Kudryashov, “Bounded limit cycles of polynomial foliations in ℂ²” Bulletin of the Brazilian Mathematical Society, New Series (2017) Volume 48, Issue 1, pp 63–83.
  • N. Goncharuk, Yu. Kudryashov, “Cheap complex limit cycles” (arXiv:1702.00897), Nonlinearity, Volume 31, Number 3 (2018).
  • N. Goncharuk, Yu. Kudryashov, “Genera of non-algebraic leaves of polynomial foliations of ℂ²” (arXiv:1407.7878), accepted to Moscow Mathematical Journal.

Bifurcations of vector fields:

  • N.Goncharuk, Yu. Ilyashenko, “Large bifurcation supports”, arXiv:1804.04596.

  • N.Goncharuk, Yu. Ilyashenko, N.Solodovnikov, “Global bifurcations in generic one-parameter families with a parabolic cycle on S2” ( arXiv:1707.09779), submitted.

Teaching aids:

  • Lecture notes of the course Ordinary differential equations, part I (with A. I. Bufetov and  Yu.S.Ilyashenko) (in Russian), Moscow:the Board of Trustees of the Department of Mechanics and Mathematics of MSU, 2012. — 120 p.