Michael Yampolsky

Office: BA6122, UTM - 4061. Phone 416-978-4637 (St George), 905-828-5356 (UTM); Fax 416-978-4107

E-mail: yampol at math dot toronto dot edu

Click here for the course materials for MAT 252, Spring 2008

Click here for the course materials for MAT 332, Spring 2008

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, Moscow Math. Journ., 6 (2006), no. 2. Available as e-print math.DS/0501448 at Arxiv.org

with M. Braverman, Non-computable Julia sets, Journ. Amer. Math. Soc., 19 (2006), 551-578.

with I. Binder and M. Braverman, Filled Julia sets with empty interior are computable, Journal FoCM, 7(2007), 405-416.

with I. Binder and M. Braverman, On computational complexity of Siegel Julia sets, Commun. Math. Phys., 264, 317-334(2006)

with I. Binder and M. Braverman, On computational complexity of Riemann mapping, Arkiv for Matematik, 45(2007), 221-239.

Siegel disks and renormalization fixed points, Fields Institute Communications, 53(2008)

with D. Gaidashev, Cylinder renormalization of Siegel disks, Exp. Math., 16(2007), 215-226. The software developed for this project is available here.

with M. Braverman, Computability of Julia sets, Moscow Math. Journ., to appear. Available as e-print math.DS/0610340 at Arxiv.org. Parts of this paper have been posted as preprints math.DS/0604175 and math.DS/0604371.

with M. Braverman, Constructing non-computable Julia sets, Proceedings of STOC 2007.

with M. Aspenberg, Mating non-renormalizable quadratic polynomials, Commun. Math. Phys., to appear. Available as e-print math.DS/0610343 at Arxiv.org.