Publications of Nataliya Goncharuk
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.
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• 4. N. Goncharuk, Yu. Kudryashov, “
Cheap complex limit cycles” (arXiv:1702.00897), Nonlinearity, Volume 31, Number 3 (2018).
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• 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.
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• 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.
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• 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.
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• 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.
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• 11. N. Goncharuk, Yu. Kudryashov, N. Solodovnikov, “
New structurally unstable families of planar vector fields”, arXiv:1908.02693, Nonlinearity 34:1 (2021).
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• 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.
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• 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.
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• 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, Renormalization of circle maps and smoothness of Arnold tongues,
arxiv:2307.15195, submitted.
• 17. N.Goncharuk, I.Gorbovickis, Renormalization and scaling of bubbles,
arxiv:2312.11308
, submitted.
• 18. N.Goncharuk, M.Yampolsky, Authomorphic measures with negative exponents for multicritical circle maps,
arxiv:2404.03780
, submitted.
• 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.
