Most of the papers since 1990, in their prelimenary form, can be also downloaded from
the IMS Preprint server or from the archive.

[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.

  More general unicritical dynamics

• Teichmuller space of Fibonacci maps. Preprint IMS at Stony Brook, 1993, # 12.

• Regular or stochastic dynamics in real analytic families of unimodal maps. Inventiones Math., v. 154 (2003), 451 -- 550 (joint with A. Avila and W. de Melo).

• Parapuzzle of the Multibrot set and typical dynamics of unimodal maps. Journal of European Math Soc., v. 13 (2011), 27--56. (joint with A. Avila and W. Shen).

• The full renormalization horseshoe for unimodal maps of higher degree: Exponential contraction along hybrid classes. Preprint IMS at Stony Brook, # 3 (2010), to appear in Publ. IHES. (joint with Artur Avila).
  
  Steps towards MLC

  All papers in this series are joint with Jeremy Kahn.

• Quasi-Additivity Law in conformal geometry. Annals Math., v. 169 (2009), 561--593.

• Local connectivity of Julia sets for unictritical polynomials. Annals of Math., v. 170 (2009), 413--426.

• Combinatorial rigidity for unicritical polynomials. Annals of Math., v. 170 (2009), 783--797 (joint with A. Avila and W. Shen).

• A priori bounds for some infinitely renormalizable quadratics, II. Decorations. Ann. Sci. Ecole Norm. Sup., v. 41 (2008), 57--84.

• A priori bounds for some infinitely renormalizable quadratics, III. Molecules. In: ``Complex Dynamics: Families and Friends''.
  Proceeding of the conference dedicated to Hubbard's 60th birthday (ed.: D. Schleicher). Peters, A K, Limited, 2009.
  
  Henon family, real and complex.

• Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents. Inventions Math., v. 112 (1993), 77 - 125 (joint with Eric Bedford and John Smillie).

• Distribution of periodic points of polynomial diffeomorphisms of C^2. Inventions Math., v. 114 (1993), 277 - 288 (joint with E. Bedford and J. Smillie) .

• Renormalization in the Henon family, I. Universality but non-rigidity. J. Stat.Phys., Special issue dedicated to Feigenbaum's 60th birthday, v. 121 (2005), 611--669
  (joint with A. de Carvalho and M. Martens).

• Renormalization in the Henon family, II: the heteroclinic web. Preprint IMS at Stony Brook, # 2 (2008), to appear in Inventiones Math. (joint with Marco Martens).

• Probabilistic universality on two-dimensional dynamics. Preprint IMS at Stony Brook, # 2 (2011) (joint with M. Martens).
  
  Ising model and rational dynamics

• The Julia sets and complex singularities in hierarchical Ising models, Commun. Math. Phys. v. 141 (1992), 453--474. (joint with Pavel Bleher)

• Lee-Yang zeros for DHL and 2D rational dynamics, I. Foliation of the physical cylinder. Preprint IMS at Stony Brook 2010 # 3 (joint with P. Bleher and R. Roeder)
  
  Measure and dimension of some Julia sets and parameter sets

  [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).

  Laminations

• Laminations in holomorphic dynamics. J. Diff. Geom., v. 47 (1997), 17 - 94 (joint with Yair Minsky).

• Conformal and harmonic measures on laminations associated with rational maps. Memoirs of the AMS, v. 173 (2005), No 820 (joint with Vadim Kaimanovich).

• Laminations and Holomorphic Dynamics. Lecture Notes of the mini-course given at the Conference ``New Directions in Dynamical Systems" in Kyoto, August 2002.

• A note on hyperbolic leaves and wild laminations of rational functions. Journal of Differential Equations, a volume in honor of Bob Devaney 60th birthday,
  v. 16 (2010), 655--665 (joint with J. Kahn and L. Rempe).
  
  Smooth Ergodic Theory on the interval

  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.

  No Wandering Intervals

  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).

  Transcendental Dynamics

  All papers in this section, except [4,5], are joint with Alex Eremenko.

  [1] Iterations of entire functions. Dokl. Akad. Nauk SSSR, v. 279 (1984), No 1, 25-27.

  [2] Examples of entire functions with pathological dynamics. J. London Math. Soc., v. 36 (1987), 458 - 468.

  [3] Dynamical properties of some classes of entire functions. Ann. Inst. Fourier, v. 42 (1992), No 4, 989-1020.

  [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.
  

  Structural stability of rational endomorphisms

  [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. \& Prilozh., 42 (1984), 72 - 91 (Russian).
  English translation: Selecta Mathematica Sovetica, v. 9 (1990), 69 - 90.
  

  Entropy properties of rational endomorphisms

  [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.
  

  Surveys

• The dynamics of rational transforms: the topological picture. Russian Math. Surveys, v. 41 (1986), # 4, 43--117.

• Milnor's attractors, persistent recurrence and renormalization, ``Topological Methods in Modern Mathematics, A Symposium in Honor of John Milnor's 60th Birthday",
  Publish or Perish, 1993.

• On the borderline of real and complex dynamics. Proc. ICM, Z\"urich 1994. Birkh\"auser 1995, v. 2, 1203 -- 1215.

• Renormalization ideas in conformal dynamics. Cambridge Seminar ``Current Developments in Math.", May 1995. International Press, 1995. Cambridge, MA, 155 - 184.

• Six Lectures on Real and Complex Dynamics (based on European Lectures given in Barcelona, Copenhagen and St Petersburg in May-June 1999).
  Reviews.

• Review on the books by C. McMullen ``Complex dynamics and renormalization" and ``Renormalization and 3-manifolds which fiber over the circle".
  Bulletin of the AMS, v. 36 (1999), 103 - 107.
  Almost periodic representations

  This series of papers is joint with Yuri Lyubich.

• Spectral theory of almost periodic representations of semigroups Ukrainian Math. Journal, v.36 (1984), No 5, 474--478.
  Comments