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Texas A&M Logo 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. 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, submitted.

• 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, 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.

• 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.


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