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H.C. Wang Assistant Professor
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.
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.
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.