111
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Algorithmic Construction of Hurwitz Maps

, , &

REFERENCES

  • [Atkin and Swinnerton-Dyer 71] A. Oliver L. Atkin, and H. Peter F. Swinnerton-Dyer. “Modular Forms on Noncongruence Subgroups.” In Combinatorics (Proc. Sympos. Pure Math. Vol. XIX, Univ. California, Los Angeles, Calif., 1968), pp. 1–25. Amer. Math. Soc., 1971.
  • [Bowers and Stephenson 04] Philip L. Bowers and Kenneth Stephenson. Uniformizing Dessins and Bely Maps via Circle Packing. Amer. Math. Soc., 2004.
  • [Boyd and Henriksen 12] Suzanne Hruska Boyd and Christian Henriksen. “The Medusa Algorithm for Polynomial Matings.” Conform. Geom. Dyn. 16 (2012), 161–183.
  • [Couveignes and Granboulan 94] Jean-Marc Couveignes and Louis Granboulan. “Dessins from a Geometric Point of View.” In The Grothendieck Theory of Dessins d’Enfants (Luminy, 1993), London Math. Soc. Lecture Note Ser. 200, pp. 79–113. Cambridge Univ. Press, 1994.
  • [Couveignes 97] Jean-Marc Couveignes. “Quelques revêtements définis sur .” Manuscripta Math. 92 (1997), 409–445.
  • [Doudy and Hubbard 93] Adrien Douady and John H. Hubbard. “A Proof of Thurston’s Topological Characterization of Rational Functions.” Acta Math. 171 (1993), 263–297.
  • [GAP 08] The GAP Group. “GAP — Groups, Algorithms, and Programming,” Version 4.4.10. Available at http://www.gap-system.org, 2008.
  • [Grothendieck 97] Alexandre Grothendieck. “Esquisse d’un programme.” In Geometric Galois Actions 1, London Math. Soc. Lecture Note Ser. 242, pp. 5–48, with an English translation on pp. 243–283. Cambridge Univ. Press, 1997.
  • [Hubbard and Schleicher 94] John H. Hubbard and Dierk Schleicher. “The Spider Algorithm.” In Complex Dynamical Systems (Cincinnati, OH, 1994), Proc. Sympos. Appl. Math. 49, pp. 155–180. Amer. Math. Soc., 1994.
  • [Hurwitz 91] Adolf Hurwitz. “Ueber Riemann’sche Flächen mit gegebenen Verzweigungspunkten.” Math. Ann. 39 (1891), 1–60.
  • [Kühnau 83] R. Kühnau. “Numerische Realisierung konformer Abbildungen durch ‘Interpolation.’” Z. Angew. Math. Mech. 63 (1983) 631–637.
  • [Lenstra et al. 82] Arjen K. Lenstra, Hendrik W. Lenstra Jr, and Lázló Lovász. “Factoring Polynomials with Rational Coefficients.” Math. Ann. 261 (1982), 515–534.
  • [Malle 87] Gunter Malle. “Polynomials for Primitive Nonsolvable Permutation Groups of Degree d ≤ 15.” J. Symbolic Comput. 4 (1987), 83–92.
  • [Malle and Matzat 85] Gunter Malle and Bernd H. Matzat. “Realisierung von Gruppen als Galoisgruppen über .” Math. Ann. 272 (1985), 549–565.
  • [Marshall and Rohde 07] Donald E. Marshall and Steffen Rohde. “Convergence of a Variant of the Zipper Algorithm for Conformal Mapping.” SIAM J. Numer. Anal. 45 (2007), 2577–2609 (electronic).
  • [Matiyasevich 96] Yu. V. Matiyasevich. “Computation of Generalized Chebyshev Polynomials on a Computer.” Vestnik Moskov. Univ. Ser. I Mat. Mekh. 6 (1996), 59–61, 112; English transl., Moscow Univ. Math. Bull. 51 (1996), 39–40.
  • [PARI 11] The PARI Group. “PARI/GP,” Version 2.5.0, Bordeaux. Available at http://pari.math.u-bordeaux.fr, 2011.
  • [Pilgrim 00] Kevin M. Pilgrim. “Dessins d’Enfants and Hubbard Trees.” Ann. Sci. École Norm. Sup. (4) 33 (2000), 671–693.
  • [Poirier 09] Alfredo Poirier. “Critical Portraits for Postcritically Finite Polynomials.” Fund. Math. 203 (2009), 107–163.
  • [Renka 97] Robert J. Renka. “Algorithm 772: STRIPACK: Delaunay Triangulation and Voronoi Diagram on the Surface of a Sphere.” ACM Trans. Math. Software 23 (1997), 416–434.
  • [Shewchuk 02] Jonathan R. Shewchuk. “Delaunay Refinement Algorithms for Triangular Mesh Generation.” Comput. Geom. 22 (2002), 21–74.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.