Most of the papers since 1990, in their prelimenary form,
can be also downloaded from
the
IMS Preprint server
or from the
archive.
Conformal Geometry and Dynamics of Quadratic Polynomials, vol. I--II
Analytic low-dimensional dynamics: From dimension one to two.
Proceedings of the ICM-14, v.1, 443--474.
Based on the plenary talk available on
YouTube
Renormalization of unicritical diffeomorphisms of the disk.
arXiv: 2401.13559 (2024)
(joint with S. Crovissier, E. Pujals and J. Yang).
Structure of hyperbolic polynomial automorphisms of C2 with
disconnected Julia set.>
arXiv: 2309.14135 (2023)
(joint with R. Dujardain).
Schwarz reflections and the Tricorn.
arXiv:1812.01573 (2018);
to appear in Ann. Inst. Fourier (2024)
(joint with S.-Y. Lee, N. Makarov, and S. Mukherjee).
David extension of circle homeomorphisms:
welding, mating, and removability.
arXiv:2010.11256 (2020);
to appear in Memoirs AMS (2024)
(joint with S. Merenkov, S. Mukherjee, and D. Ntalampekos).
Dynamics of Schwarz reflections: the mating phenomena.
arXiv:1811.04979 (2018);
Ann. Sci. Ec. Norm. Sup., v.56 (2023), 1825--1881
(joint with S.-Y. Lee, N. Makarov, and S. Mukherjee ).
Antiholomorphic correspondences and mating I: realization theorems.
(2023) (joint with J. Mazor and S. Mukherjee) .
Uniform a priori bounds for neutral renormalization.
(2023) (joint with Dzmitry Dudko ).
Local connectivity of the Mandelbrot set at some satellite parameters
of bounded type.
GAFA online (2023)
(joint with Dzmitry Dudko ).
On dynamical gaskets generated by rational maps, Kleinian groups,
and Schwarz reflections.
Conformal Geometry and Dynamics v.27 (2023), 1--54
(joint with R. Lodge, S. Merenkov, and S. Mukherjee ).
Self-similar groups and holomorphic dynamics:
renormalization, integrability, and spectrum.
Arnold Math. J. online (2023)
(joint with N.-B. Dang and R. Grigorchuk ).
Lebesgue measure of Feigenbaum Julia sets.
Annals. Math., v 195 (2022), 1--88 (joint with Artur Avila ).
Structure of partially hyperbolic H\'enon maps.
JEMS, v. 23 (2021), 3075--3128
(joint with Han Peters ).
Schwarz reflections and anti-holomorphic correspondences.
Advances Math., v. 385 (2021)
(joint with S.-Y. Lee, N. Makarov, and S. Mukherjee).
The critical locus of H\'enon maps.
arXiv:2101.12148 (2021)
(joint with John Robertson).
Pacman renormalization and self-similarity of the Mandelbrot set
near Siegel parameters.
JAMS, v. 33 (2020), 653--733
(joint with Dzmitry Dudko and Nikita Selinger).
Lee-Yang zeros for the Diamond Hierarchical Lattice
and 2D rational dynamics, II: Global pluripotential interpretation.
J. Geometric Analysis, v. 30 (2020), 777-833
(joint with P. Bleher and R. Roeder).
Hedgehogs for neutral dissipative germs of holomorphic
diffeomorphisms of (C2,0)
In: ``Quelques aspects de la th\'eorie des syst\`ems dynamiques:
un hommage \`a Jean-Christoph Yoccoz (vol II)''.
Asterisque, v. 416 (2020), 193--211
(joint with Tanya Firsova, Remus Radu and Raluca Tanase ).
Hedgehogs in higher dimensions and their applications
In: ``Quelques aspects de la th\'eorie des syst\`ems dynamiques:
un hommage \`a Jean-Christoph Yoccoz (vol II)''.
Asterisque, v. 416 (2020), 213--251
(joint with Remus Radu and Raluca Tanase ).
[1]
Dynamics of Schwarz reflections: the mating phenomena.
arXiv:1811.04979 (2018);
Ann. Sci. Ec. Norm. Sup., v.56 (2023), 1825--1881
(joint with S.-Y. Lee, N. Makarov, and S. Mukherjee ).
[2]
Schwarz reflections and the Tricorn.
arXiv:1812.01573 (2018);
to appear in Ann. Inst. Fourier (2024)
(joint with S.-Y. Lee, N. Makarov, and S. Mukherjee).
[3]
On dynamical gaskets generated by rational maps, Kleinian groups,
and Schwarz reflections.
Conformal Geometry and Dynamics v.27 (2023), 1--54
(joint with R. Lodge, S. Merenkov, and S. Mukherjee ).
[4]
David extension of circle homeomorphisms:
welding, mating, and removability.
arXiv:2010.11256 (2020);
to appear in Memoirs AMS (2024)
(joint with S. Merenkov, S. Mukherjee, and D. Ntalampekos).
[5]
Antiholomorphic correspondences and mating I: realization theorems.
(2023) (joint with J. Mazor and S. Mukherjee) .
[1]
The Fibonacci unimodal map.
J. Amer. Math. Soc., v. 6 (1993), # 2, 425-457
(joint with John Milnor ).
[2]
Combinatorics, geometry and attractors of quasi-quadratic maps.
Annals of Mathematics, v. 140 (1994), 347-404.
See also:
Note on the geometry of generalized parabolic towers.
[3]
Dynamics of quadratic polynomials, I-II.
Acta Mathematica, v. 178 (1997), 185-297.
[4]
Dynamics of quadratic polynomials:
Complex bounds for real maps.
Annalles de l'Institut Fourier, v. 47 (1997), # 4, 1219 - 1255
(joint with Michael Yampolsky ).
[6]
Feigenbaum-Coullet-Tresser Universality and Milnor's Hairiness Conjecture.
Annals of Mathematics, v. 149 (1999), 319 - 420.
[5]
Dynamics of quadratic polynomials III: parapuzzle and SBR measures.
Asterisque volume in honor of Adrien Douady's 60th birthday
``G\'eom\'etrie complexe et syst\'emes dynamiques'', v. 261 (2000), 173 - 200.
[7]
Almost every real quadratic map is either regular or stochastic.
Annals of Mathematics, v. 156 (2002), 1 - 78.
[8]
The quadratic family as a qualitatively solvable model of chaos.
Notices of the American Math. Society, October 2000.
All papers in this series are joint with Jeremy Kahn.
"lambda-lemma for families of Riemann surfaces and
the critical loci of complex H\'enon map"
Preprint IMS at Stony Brook, #3 (2014)
(joint with Tanya Firsova ).
[1]
Typical behaviour of trajectories of a rational mapping of the sphere.
Dokl. Akad. Nauk SSSR, v. 268 (1982), 29 - 32.
[2]
On the Lebesgue measure of the Julia set of a quadratic
polynomial.
Preprint IMS at Stony Brook, 1991, # 10.
[3]
How big is the set of infinitely renormalizable quadratics?
The volume
"Voronezh Winter Mathematical Schools"
in honor of 80th birthday of S.G. Krein.
AMS Transl. (2), v. 184 (1998), 131 - 143.
[4]
Hausdorff dimension and conformal measures of Feigenbaum Julia sets.
J. of the AMS, 21 (2008), 305--383 (joint with A. Avila ).
[5]
Lebesgue measure of Feigenbaum Julia sets.
arXiv: 1504.02986 [mathDS] (2015) (joint with Artur Avila ).
All papers in this section, except [7], are joint with Sasha Blokh.
[1]
Attractors of transformations of the interval.
Functional Analysis and Appl., v. 21 (1987), 70 - 71.
[2]
Ergodicity of transitive unimodal transformations of the
interval.
Ukrainian Math. J., v. 41 (1989), No 7, 985 - 988
[3] Attractors of maps of the interval. Banach Center Publ., v. 23 (1989), 427 - 442.
[4] On the decomposition of one-dimensional dynamical systems into
ergodic components.
Algebra and Analysis, v.1 (1989), 128 - 145.
English translation: Leningrad Math. J., v. 1 (1989), 137 - 155.
[4]
Measure of solenoidal attractors of unimodal transformations of
the interval.
Math. Notes., v. 48 (1990), No 5, 15 - 20.
[5] Measure and dimension of solenoidal attractors of
one-dimensional dynamical systems.
Comm. Math. Phys., v. 127 (1990), 573-583.
[6] Measurable dynamics of S-unimodal maps of the interval.
Annalles Scientifique Ecole Normale Sup., v. 24 (1991), 545-573.
[7]
Ergodic Theory for smooth one-dimensional dynamical systems.
Preprint IMS at Stony Brook, 1991, No 11.
Non-existence of wandering intervals and structure of topological attractors
of one-dimensional dynamical systems,
I. The case of negative Schwarzian derivative.
Ergodic Theory and Dynamical Systems, v. 9 (1989), No 4, 737-750.
Non-existence of wandering intervals and structure of topological attractors
of one-dimensional dynamical systems,
II. The smooth case.
Ergodic Theory and Dynamical Systems,
v. 9 (1989), No 4, 751 - 758 (joint with A. Blokh).
[1] Iterations of entire functions.
Dokl. Akad. Nauk SSSR, v. 279 (1984), No 1, 25-27
(joint with Alex Eremenko).
[2] Examples of entire functions with pathological dynamics.
J. London Math. Soc., v. 36 (1987), 458 - 468
(joint with Alex Eremenko).
[3] Dynamical properties of some classes of entire functions.
Ann. Inst. Fourier, v. 42 (1992), No 4, 989-1020
(joint with Alex Eremenko).
[4]
On typical behaviour of trajectories of the exponential function.
Russian Math, Surveys, v. 41 (1986), 199 - 200.
[5]
Measurable dynamics of the exponential.
Siberian Math. J., v. 28 (1987), No 5, 111 - 127.
[6]
Repelling periodic points and landing of rays for post-singularly bounded
exponential maps
Ann. Inst Fourier, v. 64 (2014), 1493--1520
(joint with Anna Benini).
[1]
Some typical properties of the dynamics of rational maps.
Russian Math. Surveys, v. 38 (1983), No 5, 154-155.
[2] An analysis of stability of the dynamics of rational functions.
Teoriya Funk., Funk. Anal. and Prilozh., 42 (1984), 72 - 91
(Russian).
English translation: Selecta Mathematica Sovetica, v. 9 (1990),
69 - 90.
[1]
Entropy of analytic endomorphisms of the Riemann sphere.
Functional Analysis & Appl., v. 15 (1981), No 4, 83-84.
[2]
The measure of maximal entropy of a rational endomorphism of the Riemann sphere.
Functional Analysis and Appl., v. 16 (1982), No 4, 78 - 79.
[3] Entropy properties of rational endomorphisms of the Riemann sphere.
Ergodic Theory & Dynamical Systems, v. 3 (1983), No 3, 351-385.
On the logarithmic property of the degree of a finite group.
Dokl. Akad. Nauk SSSR, v. 247 (1979), 791--794.
On cycles and coverings associated to a knot.
arXiv math 1 301.2205v1 (2013)
(joint with Lilya Lyubich).
Quasisymmetries of Sierpinski carpet Julia sets
Preprint IMS at Stony Brook, #1 (2014)
(joint with Mario Bonk and Sergei Merenkov> )
This series of papers is joint with Yuri Lyubich.