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Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe

Collection Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe

Organisateur(s) Benini, Anna Miriam ; Drach, Kostiantyn ; Dudko, Dzmitry ; Hlushchanka, Mikhail ; Schleicher, Dierk
Date(s) 20/09/2021 - 24/09/2021
URL associée https://conferences.cirm-math.fr/2546.html
00:00:00 / 00:00:00
7 27

Characterizing Thurston maps by lifting trees

De Rebecca Winarski

Thurston proved that a post-critically finite branched cover of the plane is either equivalent to a polynomial (that is: conjugate via a mapping class) or it has a topological obstruction. We use topological techniques — adapting tools used tostudy mapping class groups — to produce an algorithm that determines when a branched cover is equivalent to a polynomial, and if it is, determines which polynomial a branched cover is equivalent to. This is joint work with Jim Belk, Justin Lanier, and Dan Margalit.

Informations sur la vidéo

Données de citation

  • DOI 10.24350/CIRM.V.19816103
  • Citer cette vidéo Winarski, Rebecca (23/09/2021). Characterizing Thurston maps by lifting trees. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19816103
  • URL https://dx.doi.org/10.24350/CIRM.V.19816103

Domaine(s)

Bibliographie

  • BELK, James, LANIER, Justin, MARGALIT, Dan, et al. Recognizing topological polynomials by lifting trees. arXiv preprint arXiv:1906.07680, 2019. - https://arxiv.org/abs/1906.07680
  • BARTHOLDI, Laurent et DUDKO, Dzmitry. Algorithmic aspects of branched coverings. In : Annales de la Faculté des sciences de Toulouse: Mathématiques. 2017. p. 1219-1296. - https://doi.org/10.5802/afst.1566
  • BARTHOLDI, Laurent et NEKRASHEVYCH, Volodymyr. Thurston equivalence of topological polynomials. Acta mathematica, 2006, vol. 197, no 1, p. 1-51. - http://dx.doi.org/10.1007/s11511-006-0007-3
  • BELK, James, LANIER, Justin, MARGALIT, Dan, et al. Recognizing topological polynomials by lifting trees. arXiv preprint arXiv:1906.07680, 2019. - https://arxiv.org/abs/1906.07680
  • BIELEFELD, Ben, FISHER, Yuval, et HUBBARD, John. The classification of critically preperiodic polynomials as dynamical systems. Journal of the American Mathematical Society, 1992, vol. 5, no 4, p. 721-762. - https://doi.org/10.2307/2152709
  • BONNOT, Sylvain, BRAVERMAN, Mark, et YAMPOLSKY, Michael. Thurston equivalence to a rational map is decidable. arXiv preprint arXiv:1009.5713, 2010. - https://arxiv.org/abs/1009.5713
  • CANNON, James, FLOYD, William, PARRY, Walter, et al. Nearly Euclidean Thurston maps. Conformal Geometry and Dynamics of the American Mathematical Society, 2012, vol. 16, no 12, p. 209-255. - http://dx.doi.org/10.1090/S1088-4173-2012-00248-2
  • CHEN, Lei, KORDEK, Kevin, et MARGALIT, Dan. Homomorphisms between braid groups. arXiv preprint arXiv:1910.00712, 2019. - https://arxiv.org/abs/1910.00712
  • DOUADY, Adrien et HUBBARD, John H. Etude dynamique des polynômes complexes. Partie I, volume 84 of Publications Mathématiques d'Orsay. 1984.
  • DOUADY, Adrien et HUBBARD, John H. Étude dynamique des polynômes complexes. Partie II. With the collaboration of P. Lavaurs, Tan Lei and P. Sentenac. Publications Mathématiques d'Orsay, 1985, vol. 85, no 4.
  • DOUADY, Adrien et HUBBARD, John H. A proof of Thurston's topological characterization of rational functions. Acta Mathematica, 1993, vol. 171, no 2, p. 263-297. - http://dx.doi.org/10.1007/BF02392534
  • FLOYD, William, PARRY, Walter, et PILGRIM, Kevin M. Modular groups, Hurwitz classes and dynamic portraits of NET maps. Groups, Geometry, and Dynamics, 2018, vol. 13, no 1, p. 47-88. - https://doi.org/10.4171/ggd/479
  • FLOYD, William, PARRY, Walter, et PILGRIM, Kevin M. Rationality is decidable for nearly Euclidean Thurston maps. Geometriae Dedicata, 2021, p. 1-26. - https://doi.org/10.1007/s10711-020-00593-9
  • HLUSHCHANKA, Mikhail. Invariant graphs, tilings, and iterated monodromy groups. 2017. Thèse de doctorat. Jacobs University Bremen. - http://nbn-resolving.org/urn:nbn:de:gbv:579-opus-1007507
  • HUBBARD, John et MASUR, Howard. Quadratic differentials and foliations. Acta Mathematica, 1979, vol. 142, no 1, p. 221-274. - http://dx.doi.org/10.1007/BF02395062
  • KELSEY, Gregory et LODGE, Russell. Quadratic Thurston maps with few postcritical points. Geometriae Dedicata, 2019, vol. 201, no 1, p. 33-55. - https://doi.org/10.1007/s10711-018-0387-5
  • LEVY, Silvio Vieira Ferreira. Critically finite rational maps (Thurston). 1985. Thèse de doctorat. Princeton University.
  • LODGE, Russell. Boundary values of the Thurston pullback map. Conformal Geometry and Dynamics of the American Mathematical Society, 2013, vol. 17, no 8, p. 77-118. - http://dx.doi.org/10.1090/S1088-4173-2013-00255-5
  • NEKRASHEVYCH, Vladimir. Personal communication, 2020.
  • Volodymyr Nekrashevych. Combinatorics of polynomial iterations. In Complex dynamics, pages 169-214. A K Peters, Wellesley, MA, 2009.
  • NEKRASHEVYCH, Volodymyr. Combinatorial models of expanding dynamical systems. Ergodic Theory and Dynamical Systems, 2014, vol. 34, no 3, p. 938-985. - https://doi.org/10.1017/etds.2012.163
  • PFRANG, David, ROTHGANG, Michael, et SCHLEICHER, Dierk. Homotopy Hubbard Trees for post-singularly finite exponential maps. arXiv preprint arXiv:1812.11831, 2018. - https://arxiv.org/abs/1812.11831
  • PILGRIM, Kevin M. et LEI, Tan. Combining rational maps and controlling obstructions. Ergodic Theory and Dynamical Systems, 1998, vol. 18, no 1, p. 221-245. - https://doi.org/10.1017/S0143385798100329
  • RAFI, Kasra, SELINGER, Nikita, et YAMPOLSKY, Michael. Centralizers in Mapping Class Groups and Decidability of Thurston Equivalence. Arnold Mathematical Journal, 2020, vol. 6, no 2, p. 271-290 - https://doi.org/10.1007/s40598-020-00150-y
  • SELINGER, Nikita et YAMPOLSKY, Michael. Constructive geometrization of Thurston maps, C. R. Math. Rep. Acad. Sci. Canada, 2015, vol. 37 n°3, p. 100-113. - https://mr.math.ca/article/constructive-geometrization-of-thurston-maps/
  • SHEPELEVTSEVA, Anastasia et TIMORIN, Vladlen. Invariant spanning trees for quadratic rational maps. Arnold Mathematical Journal, 2019, vol. 5, no 4, p. 435-481. - https://doi.org/10.1007/s40598-019-00123-w

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