Office: BA6122 (St George), DH3022 (UTM). Phone 416-978-4637 (St George), 905-828-5356 (UTM); Fax 416-978-4107
E-mail: yampol at math dot toronto dot edu
- 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),
- 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
- 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., to appear.
- with D. Gaidashev, Golden mean Siegel disk universality and renormalization, e-print ArXiv:1604.00717
- with D. Gaidashev, Renormalization of almost commuting pairs, Inventiones Math., to appear
- with R. Radu and D. Gaidashev, Renormalization and Siegel disks for complex Henon maps, JEMS, to appear
- with J. Yang, The boundaries of golden-mean Siegel disks in the complex quadratic Henon family are not smooth, proceedings of Welington de Melo 70th birthday conference, Springer, to appear
- 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, to appear.
- 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,
Handbook on computability and complexity in analysis, to appear.
- with I. Binder and C. Rojas Caratheodory convergence and harmonic measure, Potential analysis, 2018.
- with K. Rafi and N. Selinger Centralizers in Mapping Class Group and decidability of Thurston Equivalence , e-print ArXiv:1902.02645
- with C. Rojas Real quadratic Julia sets can have arbitrarily high complexity, e-print ArXiv:1904.06204
- with A. Dudko On computational complexity of Cremer Julia sets, Fundamenta
Mathematicae, to appear.
- with J. Yang Structural Instability of Semi-Siegel Henon maps, e-print, Arxiv:1908.06465
- 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, e-print, Arxiv:1910.09625
- 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