Michael Yampolsky

Professor, Department of Mathematics

Office: BA6122 (St George), DH3022 (UTM). E-mail: yampol at math dot toronto dot edu

Books:

Mathematical modeling in life sciences: an introduction, Amazon, 2021
O. Lanford III and M. Yampolsky, Fixed Point of the Parabolic Renormalization Operator, Series: SpringerBriefs in Mathematics, Vol. VIII, Springer, 2014.
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., Volume 12(2012), 747-763.
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, Math. Reports, 34(2012)
with I. Binder and C. Rojas, Computable Caratheodory Theory, Advances in Math., 265(2014), 280-312.
with N. Selinger, Constructive geometrization of Thurston maps and decidability of Thurston equivalence, Arnold Math. Journal, 1(4), 361-402.
with K. Khanin, Hyperbolicity of renormalization of circle maps with a break-type singularity, Moscow Math. J., 15(2015), 1-15
with I. Binder and C. Rojas, Non-computable impressions of computable external rays of quadratic polynomials, Commun. Math. Phys., Volume 335, Issue 2, pp 739-757
with A. Dudko, Poly-time Computability of the Feigenbaum Julia set, Ergodic Theory and Dynam. Sys., Volume 36, Issue 8 December 2016, pp. 2441-2462
with N. Selinger, Constructive geometrization of Thurston maps, Math. Reports, 37(3), 100-113, 2015
with I. Gorbovickis, Rigidity, universality, and hyperbolicity of renormalization for critical circle maps with non-integer exponents, Ergodic theory and dynam. sys., 40(5), (2020), pp. 1282-1334.
with D. Gaidashev, Golden mean Siegel disk universality and renormalization, Moscow Math. J., 22(3), 451-491, 2022
with D. Gaidashev, Renormalization of almost commuting pairs, Inventiones Math., 221(2020), 203-236
with R. Radu and D. Gaidashev, Renormalization and Siegel disks for complex Henon maps, JEMS, 2020
with J. Yang, The boundaries of golden-mean Siegel disks in the complex quadratic Henon family are not smooth, New Trends in One-Dimensional Dynamics (proceedings of Welington de Melo 70th birthday conference), 2019, Springer, pp 301-324
Renormalization of unicritical analytic circle maps, C.R. Math. Rep. Acad. Sci. Canada, Vol. 39(3), 2017, pp. 77-89
with I. Gorbovickis, Renormalization for unimodal maps with non-integer exponents, Arnold Math. Journal, 2018 vol. 4, 179-191
with A. Dudko, Almost every real quadratic polynomial has a poly-time computable Julia set, J. FoCM, 2017.
with D. Coronel and C. Rojas, Non computable Mandelbrot-like set for a one-parameter complex family, Information and Computation, Volume 262, Part 1, October 2018, Pages 110-122.
with C. Rojas, Computational intractability of attractors in the real quadratic family, Advances in Math., vol. 349, 2019, 941-958
with C. Rojas, Computable geometric complex analysis and complex dynamics, in Handbook on computability and complexity in analysis, Springer, 2021
with I. Binder and C. Rojas Caratheodory convergence and harmonic measure, Potential analysis, 51(2019), 499-509.
with K. Rafi and N. Selinger Centralizers in Mapping Class Group and decidability of Thurston Equivalence , Arnold Mathematical Journal, volume 6, 271-290(2020)
with C. Rojas Real quadratic Julia sets can have arbitrarily high complexity, J. FoCM, 2020
with A. Dudko On computational complexity of Cremer Julia sets, Fundamenta Mathematicae, 252 (2021), 343-353
with J. Yang Structural Instability of Semi-Siegel Henon maps, Advances in Math., 389(2021)
Renormalization of bi-cubic circle maps, C. R. Math. Rep. Acad. Sci. Canada Vol. 41 (4) 2019, pp. 57
with C. Rojas How to lose at Monte Carlo: a simple dynamical system whose typical statistical behavior is non computable, STOC 2020: Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing, pp. 1066-1072
with N. Goncharuk Analytic linearization of conformal maps of the annulus, Advances in Math., 2022(409)
with G. Estevez, D. Smania Renormalization of multicritical circle maps with bounded type rotation numbers, Bulletin of the Brazilian Mathematical Society, New Series 53 (3), 1053-1071
with I. Binder, A. Glucksam, C. Rojas Computability in Harmonic Analysis, J. FoCM, 3(2022)
KAM-renormalization and Herman Rings for 2D Maps, C. R. Math. Rep. Acad. Sci. Canada Vol. 43 (2) 2021, pp. 78-86
Towards understanding the theoretical challenges of numerical modeling of dynamical systems, New Zealand Journal of Math., Vaughan Jones Memorial Special Issue, 52 (2021), 453-467,
with G. Estevez Hyperbolicity of Renormalization for bi-cubic circle maps with bounded combinatorics, C. R. Math. Rep. Acad. Sci. Canada Vol. 45 (3) 2023, pp. 64
with I. Gorbovickis Rigidity of analytic and smooth bi-cubic multicritical circle maps with bounded type rotation numbers, e-print, ArXiv:2112.05845
with N. Goncharuk Renormalization of circle maps and smoothness of Arnold tongues, Ergodic Th. and Dynam. Sys., to appear
with N. Goncharuk Authomorphic measures with negative exponents for multicritical circle maps, DCDS, to appear

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, Vol. 34, Issue 4, Pages 391-393.
M. Yampolsky, C.M. Salafia, O. Shlakhter Probability distributions of placental morphological measurements and origins of variability of placental shapes Placenta Vol. 34, Issue 6, Pages 493-496.
M. Gasperowicz, M. Yampolsky, C.M. Salafia Metabolic scaling law for mouse fetal and placental weight. Placenta, Vol. 34, Issue 11, Pages 1099-1101
M. Yampolsky, O. Shlakhter, D. Deng, S. Kala, S.L. Walmsley, K.E. Murphy,M.H. Yudin, J. MacGillivray, M. Loutfy, C. Dunk, L. Serghides Exploring the impact of HIV infection and antiretroviral therapy on placenta morphology, Placenta, Volume 104, 15 January 2021, Pages 102-109