Publications

Publications in Dynamical Systems 

1. (with N. Goncharuk) Renormalization and scaling of bubbles, (submitted) 2023, 30 pages   arXiv:2312.11308

2. (with X. Buff and V. Huguin) Entire maps with rational preperiodic points and multipliers, (submitted) 2023, 19 pages   arXiv:2304.13674

3. (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

4. (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

5. (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

6. (with D. Gaidashev) Complex a priori bounds for Lorenz maps, Nonlinearity 34 (2021), no. 3, 1263-1287   arXiv:2002.05807

7. (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

8. (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

9. (with M. Yampolsky) Renormalization of unimodal maps with non-integer exponents, Arnold Math. Journal 4 (2018), no. 2, 179-191.   arXiv:1702.01214

10. (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 

11. 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 

12. 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 

13. On multi-dimensional Fatou bifurcation, Bull. Sci. Math. 2014, (138), no. 3, 356-375. 

14. 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 

15. Normal forms of families of maps in the Poincaré domain, Proc. Steklov Inst. Math. 2006, no. 3 (254), 94-102.

Publications in Discrete Geometry 

1. The central set and its application to the Kneser-Poulsen conjecture, Discrete Comput. Geom. 59 (2018), no. 4, 784-801   arXiv:1511.08134 

2. Kneser-Poulsen conjecture for a small number of intersections, Contrib. Discrete Math. 2014, (9), no. 1, 1-10.  arXiv:1006.0529 

3. Strict Kneser-Poulsen conjecture for large radii, Geom. Dedicata 2013, (162), 95-107.   arXiv:1006.0531