Dynamics of unicritical polynomials (real and complex).
- (joint with John Milnor) The Fibonacci unimodal map.
J. Amer. Math. Soc., v. 6 (1993), 425-457.
- 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.
-
Dynamics of quadratic polynomials, I-II.
Acta Mathematica, v. 178 (1997), 185-297.
-
(joint with Michael Yampolsky) Dynamics of quadratic polynomials:
Complex bounds for real maps.
Annalles de l'Institut Fourier, v. 47 (1997), \# 4, 1219 - 1255.
-
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.
-
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.
-
Feigenbaum-Coullet-Tresser Universality and Milnor's Hairiness Conjecture.
Annals of Mathematics, v. 149 (1999), 319 - 420.
-
Almost every real quadratic map is either regular or stochastic.
Annals of Mathematics, v. 156 (2002), 1 - 78.
-
(joint with A. Avila and W. de Melo)
Regular or stochastic dynamics in real analytic families of unimodal maps.
Preprint IMS at Stony Brook, #2001/15.
-
Hausdorff dimension and conformal measures of Feigenbaum Julia sets
(joint with Artur Avila). Journal of the AMS, 21 (2008), 305--383.
-
Quasi-Additivity Law in conformal geometry
(joint with Jeremy Kahn). Annals of Mathematics , 169 (2009), 561--593.
-
Local connectivity of Julia sets for unictritical polynomials
(joint with Jeremy Kahn). Annals of Mathematics, 170 (2009), 413--426.
-
Combinatorial rigidity for unicritical polynomials
(joint with A. Avila, J. Kahn and W. Shen). Annals of Mathematics, 170 (2009), 783--797.
Two-dimensional dynamics (real and complex).
- (joint with Eric Bedford \& John Smillie)
Polynomial diffeomorphisms of ${\bf C}^2$, IV:
The measure of maximal entropy and laminar currents.
Inventions Math., v. 112 (1993), 77 - 125.
- (joint with Eric Bedford \& John Smillie) Distribution of periodic points of
polynomial diffeomorphisms of ${\bf C}^2$.
Inventions Math., v. 114 (1993), 277 - 288.
-
Renormalization in the H\'enon family
(joint with Andre de Carvalho and Marco Martens).
Journal of Statistical Physics: Special issue dedicated to Feigenbaum's 60th birthday, v. 121 (2006), 611--669.
Laminations.
-
(joint with Yair Minsky) Laminations in holomorphic dynamics.
J. Diff. Geom., v. 47 (1997), 17 - 94.
-
(joint with Vadim Kaimanovich) Conformal and harmonic measures on
laminations associated with rational maps.
Preprint IMS at Stony Brook #2001/5.
-
Laminations and Holomorphic Dynamics.
Lecture Notes of the mini-course given at the Conference
``New Directions in Dynamical Systems" in Kyoto, August 2002.
Surveys
- 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.
-
The quadratic family as a qualitatively solvable model of chaos.
Notices of the American Math. Society, October 2000.
-
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.
Remark. The above papers (with underlined titles) are stored as compressed postscript files.
To get a file click on its title.
To uncompress the file, use command ``gunzip". For example, the paper
``Feigenbaum-Coullet-Tresser Universality..." is stored as ``universe.ps.gz".
By means of ``gunzip universe.ps.gz" you will create a postscript file
named ``universe.ps". It can be then printed out by standard means.