Publications of Nataliya Goncharuk [Back to My Home Page]

  1. N. Goncharuk, “Rotation numbers and moduli of elliptic curves”, Functional Analysis and Its Applications, 2012, 46:1, pp. 11–25. (translated from Russian)

  2. X. Buff, N. Goncharuk, “Complex rotation numbers”, Journal of Modern Dynamics, Volume 9(2015), pp. 169-190.

  3. N. Goncharuk, Yu. Kudryashov, “Bounded limit cycles of polynomial foliations in C2” Bulletin of the Brazilian Mathematical Society, New Series (2017) Volume 48, pp. 63–83. PDF

  4. N. Goncharuk, Yu. Kudryashov, “Cheap complex limit cycles” (arXiv:1702.00897), Nonlinearity, Volume 31, Number 3 (2018). PDF

  5. N. Goncharuk, Yu. Kudryashov, “Genera of non-algebraic leaves of polynomial foliations of C2” (arXiv:1407.7878), Moscow Math. J., Volume 18, Issue 1, 2018, pp. 63–83. PDF

  6. N. Goncharuk, “Complex rotation numbers: bubbles and their intersections”, Analysis and PDE, Volume 11, No 7(2018), pp. 1787 – 1801.

  7. N. Goncharuk, “Self-similarity of bubbles”, arxiv:1805.04769, Nonlinearity 32 (2019), 2496-2521. PDF

  8. N.Goncharuk, Yu. Ilyashenko, N.Solodovnikov, “Global bifurcations in generic one parameter families with a parabolic cycle on S2” (arXiv:1707.09779), Moscow Math. J., Volume 19, Issue 4, October–December 2019, pp. 709–737. PDF

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

  10. N. Goncharuk and Yu. Kudryashov, “Bifurcations of the Polycycle “Tears of the Heart”: Multiple Numerical Invariants” (arXiv:1808.07459), Moscow Math. J., Volume 20, Issue 2, April– June 2020, pp. 323–341. PDF

  11. N. Goncharuk, Yu. Kudryashov, N. Solodovnikov, “New structurally unstable families of planar vector fields”, arXiv:1908.02693, Nonlinearity 34:1 (2021). PDF

  12. N. Goncharuk, Yu. Kudryashov, “Families of vector fields with many numerical invariants”, arXiv:2003.01269, Discrete and Continuous Dynamical Systems, doi: 10.3934/dcds.2021114.

  13. N.Goncharuk, Yu. Ilyashenko, “Various Equivalence Relations in Global Bifurcation Theory”, Proceedings of the Steklov Institute of Mathematics, 2020, vol. 310, p. 78–97. PDF

  14. N.Goncharuk, M.Yampolsky, “Analytic linearization of conformal maps of the annulus”, arXiv:2004.05126, Advances in Mathematics, Volume 409, Part A, 2022, 108636, ISSN 0001-8708, https://doi.org/10.1016/j.aim.2022.108636. PDF

  15. N.Goncharuk, K.Khanin, Yu. Kudryashov, Circle homeomorphisms with breaks with no C^(2−ν) conjugacy, arxiv:2112.02765, Journal of Modern Dynamics, 2023, 19: 751-772.

  16. N.Goncharuk, M.Yampolsky, Authomorphic measures with negative exponents for multicritical circle maps, Discrete and Continuous Dynamical Systems, 2024, https://www.aimsciences.org/article/doi/10.3934/dcds.2024169, see also arxiv:2404.03780 .

  17. N.Goncharuk, M.Yampolsky, Renormalization of circle maps and smoothness of Arnold tongues, Ergodic Theory and Dynamical Systems, 2025, https://doi.org/10.1017/etds.2025.2, see also arxiv:2307.15195.

  18. N.Goncharuk, I.Gorbovickis, Renormalization and scaling of bubbles, arxiv:2312.11308 , submitted.

  19. N.Goncharuk, Anti-classification for flows on two-tori, arxiv:2503.18847 , accepted to Arnold Mathematical Journal.

Lecture notes (in Russian):


A. I. Bufetov, N.B.Goncharuk, Yu.S.Ilyashenko, Lecture notes of the course “Ordinary differential equations”, part I, Moscow: the Board of Trustees of the Department of Mechanics and Mathematics of MSU, 2012. — 120 p.