Michael Yampolsky

Professor, Department of Mathematics

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

Teaching:

MAT 242H5F (UTM) and MAT 332H5F (UTM)

Books:

M. Braverman and M. Yampolsky, "Computability of Julia sets", Series: Algorithms and Computation in Mathematics, Vol. 23, Springer, 2008.
Fields Institute Communications 53(2008): "Holomorphic Dynamics and Renormalization A Volume in Honour of John Milnor's 75th Birthday". M. Lyubich, M. Yampolsky, Editors.

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, 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., 8(2008).
with M. Braverman, Constructing non-computable Julia sets, Proceedings of STOC 2007.
with M. Aspenberg, Mating non-renormalizable quadratic polynomials, Commun. Math. Phys., 287(2009), p.1-40
with M. Braverman, Constructing Locally Connected Non-Computable Julia Sets , Commun. Mah. Phys., 291(2009), p. 513-532
with S. Bonnot and M. Braverman, Thurston equivalence to a rational map is decidable, Moscow Math. J., to appear
with I. Binder, M. Braverman, and C. Rojas, Computability of Brolin-Lyubich measure, Commun. Math. Phys. Volume 308(2011), Number 3, pp. 743-771
with S. Bonnot, Geometrization of postcritically finite branched coverings, e-print arXiv:1102.2247
with O. Lanford, The fixed point of the parabolic renormalization operator, e-print arXiv:1108.2801
with I. Binder and C. Rojas, Computable Caratheodory Theory, e-print arXiv:1209.6096

Mathematical Medicine/Biology

M. Yampolsky, C. Salafia, O. Shlakhter, D. Haas, B. Eucker, J. Thorp. Modeling the variability of shapes of a human placenta, Placenta, 29(2008), 790 - 797
C. Salafia, D. Misra, M. Yampolsky, A. Charles, R. Miller. Allometric metabolic scaling and fetal and placental weight, Placenta, 30(2009), 355-360.
C. Salafia, M. Yampolsky. Metabolic scaling law for fetus and placenta, Placenta, 30(2009), 468-471.
M. Yampolsky, O. Shlakhter, C. Salafia, D. Haas. Mean surface shape of a human placenta, e-print Arxiv.org, 0807.2995
M. Yampolsky, C. Salafia, O. Shlakhter, D. Haas, B. Eucker, J. Thorp. Centrality Of The Umbilical Cord Insertion In A Human Placenta Influences The Placental Efficiency, Placenta, 30 (2009) 1058-1064.
C. Salafia, M. Yampolsky, O. Shlakhter, D. Haas, B. Eucker, J. Thorp. Placental surface shape, function, and effects of maternal and fetal vascular pathology. Placenta, 31 (2010):958-62
M. Yampolsky, C. Salafia, O. Shlakhter, D. Misra, D. Haas, B. Eucker, J. Thorp. Variable placental thickness affects placental functional efficiency independent of other placental shape abnormalities Journal of Developmental Origins of Health and Disease (2011) Volume 2, Issue 04, pp 205 - 211, Cambridge University Press.
C.M. Salafia, M. Yampolsky, A. Shlakhter, D.H. Mandel, N. Schwartz. Variety in placental shape: When does it originate? Placenta, Volume 33, Issue 3, March 2012, Pages 164-170.
M. Yampolsky, C.M. Salafia, D.P. Misra, O. Shlakhter, J.S. Gill Is the placental disk really an ellipse? Placenta, in press.