Publications and Preprints
- with I. Chervoneva and V.M. Kadets On the upper majorant property, Quaestiones Math., 20(1997), 29-43.
- with M. Lyubich, Dynamics of quadratic polynomials: Complex bounds for real maps, Ann. Inst. Fourier (Grenoble) 47(1997), no. 4, 1219--1255
- Complex bounds for renormalization of critical circle maps,
Ergodic Theory and Dynamical Systems 18(1998), 1-31.
- with A. Epstein Geography of the cubic connectedness locus I: Intertwining surgery, Ann. Scient. Ec. Norm. Sup., 4e serie, t. 32, 1999, 151-185.
- with S. Zakeri Mating Siegel quadratic polynomials, Journ. Amer. Math. Soc., 14(2000),
25-78
- The attractor of renormalization and rigidity of towers of critical circle maps, Commun. Math. Physics, 218(2001), 537-568.
- Hyperbolicity of renormalization of critical circle maps, Publ. Math. Inst. Hautes Etudes Sci. No. 96 (2002), 1--41
- with A. Epstein The universal parabolic map, Ergodic Theory and Dynam. Systems, to appear.
- Global renormalization horseshoe for critical circle maps, Commun. Math. Physics, 240(2003), 75--96.
- Complex bounds revisited, Ann. Fac. Sci. Toulouse Math, 12 (2003), no. 4, p.533-547.
- On the eigenvalues of a renormalization operator, Nonlinearity 16 (2003), no. 5,
1565--1571. (This is an updated version)
- Unimodal maps and hierarchical models.
Graphs and Patterns in mathematical and theoretical physics, 339-357, Proc. Symp. Pure Math.AMS, 73.
- with D. Khmelev, Rigidity problem for analytic critical circle
maps. e-print math.DS/0501448 at Arxiv.org
- with M. Braverman,
Non-computable Julia sets, Journ. Amer. Math. Soc., to appear. Available as e-print math.DS/0406416 at Arxiv.org
- with I. Binder and M. Braverman, Filled Julia sets with empty interior are computable,
e-print math.DS/0410580 at Arxiv.org.
- with I. Binder and M. Braverman, On computational complexity of Siegel Julia sets,
e-print math.DS/0502354 at Arxiv.org.