Publications
Publications in Dynamical Systems
(with N. Goncharuk) Renormalization and scaling of bubbles, (submitted) 2023, 30 pages arXiv:2312.11308
(with X. Buff and V. Huguin) Entire maps with rational preperiodic points and multipliers, (submitted) 2023, 19 pages arXiv:2304.13674
(with A. Dudko and W. Tucker) Lower bounds on the Hausdorff dimension of some Julia sets, Nonlinearity 36 (2023), no. 5, 2867-2893 arXiv:2204.07880
(with M. Yampolsky) Rigidity of analytic and smooth bi-cubic multicritical circle maps with bounded type rotation numbers, (submitted) 2021, 41 pages arXiv:2112.05845
(with T. Firsova) Accumulation set of critical points of the multipliers in the quadratic family, Ergodic Theory Dynam. Systems 43 (2023), no. 5, 1548-1569 arXiv:2005.00665
(with D. Gaidashev) Complex a priori bounds for Lorenz maps, Nonlinearity 34 (2021), no. 3, 1263-1287 arXiv:2002.05807
(with T. Firsova) Equidistribution of critical points of the multipliers in the quadratic family, Adv. Math. 380, (2021), Paper No. 107591, 29 pages arXiv:1903.00062
(with A. Belova) Critical points of the multiplier map for the quadratic family, Experimental Mathematics 31, (2022), no. 1, 337-345, DOI: https://doi.org/10.1080/10586458.2019.1627682, arXiv:1902.10444
(with M. Yampolsky) Renormalization of unimodal maps with non-integer exponents, Arnold Math. Journal 4 (2018), no. 2, 179-191. arXiv:1702.01214
(with M. Yampolsky) Rigidity, universality, and hyperbolicity of renormalization for critical circle maps with non-integer exponents, Ergodic Theory Dynam. Systems 40 (2020), no. 5, 1282-1334. arXiv:1505.00686
Algebraic independence of multipliers of periodic orbits in the space of rational maps of the Riemann sphere, Mosc. Math. J. 2015, (15), no. 1, 73-87. arXiv:1401.4713
Algebraic independence of multipliers of periodic orbits in the space of polynomial maps of one variable, Ergodic Theory Dynam. Systems 36 (2016), no. 4, 1156-1166. arXiv:1305.0867
On multi-dimensional Fatou bifurcation, Bull. Sci. Math. 2014, (138), no. 3, 356-375.
Parameterizing degree n polynomials by multipliers of periodic orbits, C. R. Math. Acad. Sci. Soc. R. Can. 2013, (35), no. 4, 148-154. arXiv:1310.6830
Normal forms of families of maps in the Poincaré domain, Proc. Steklov Inst. Math. 2006, no. 3 (254), 94-102.
Publications in Discrete Geometry
The central set and its application to the Kneser-Poulsen conjecture, Discrete Comput. Geom. 59 (2018), no. 4, 784-801 arXiv:1511.08134
Kneser-Poulsen conjecture for a small number of intersections, Contrib. Discrete Math. 2014, (9), no. 1, 1-10. arXiv:1006.0529
Strict Kneser-Poulsen conjecture for large radii, Geom. Dedicata 2013, (162), 95-107. arXiv:1006.0531