Lattès maps and finite subdivision rules
HTML articles powered by AMS MathViewer
- by J. W. Cannon, W. J. Floyd and W. R. Parry
- Conform. Geom. Dyn. 14 (2010), 113-140
- DOI: https://doi.org/10.1090/S1088-4173-10-00203-1
- Published electronically: April 28, 2010
- PDF | Request permission
Abstract:
This paper is concerned with realizing Lattès maps as subdivision maps of finite subdivision rules. The main result is that the Lattès maps in all but finitely many analytic conjugacy classes can be realized as subdivision maps of finite subdivision rules with one tile type. An example is given of a Lattès map which is not the subdivision map of a finite subdivision rule with either (i) two tile types and 1-skeleton of the subdivision complex a circle or (ii) one tile type.References
- M. Bonk and D. Meyer, Expanding Thurston maps, in preparation.
- A. I. Borevich and I. R. Shafarevich, Number theory, Pure and Applied Mathematics, Vol. 20, Academic Press, New York-London, 1966. Translated from the Russian by Newcomb Greenleaf. MR 0195803
- J. W. Cannon, W. J. Floyd, and W. R. Parry, Expansion complexes for finite subdivision rules. I, Conform. Geom. Dyn. 10 (2006), 63–99. MR 2218641, DOI 10.1090/S1088-4173-06-00126-3
- J. W. Cannon, W. J. Floyd, and W. R. Parry, Constructing subdivision rules from rational maps, Conform. Geom. Dyn. 11 (2007), 128–136. MR 2329140, DOI 10.1090/S1088-4173-07-00167-1
- J. W. Cannon, W. J. Floyd, W. R. Parry, and K. M. Pilgrim, Subdivision rules and virtual endomorphisms, Geom. Dedicata 141 (2009), 181–195. MR 2520071, DOI 10.1007/s10711-009-9352-7
- Adrien Douady and John H. Hubbard, A proof of Thurston’s topological characterization of rational functions, Acta Math. 171 (1993), no. 2, 263–297. MR 1251582, DOI 10.1007/BF02392534
- John Milnor, Pasting together Julia sets: a worked out example of mating, Experiment. Math. 13 (2004), no. 1, 55–92. MR 2065568, DOI 10.1080/10586458.2004.10504523
Bibliographic Information
- J. W. Cannon
- Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
- Email: cannon@math.byu.edu
- W. J. Floyd
- Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061
- MR Author ID: 67750
- Email: floyd@math.vt.edu
- W. R. Parry
- Affiliation: Department of Mathematics, Eastern Michigan University, Ypsilanti, Michigan 48197
- MR Author ID: 136390
- Email: walter.parry@emich.edu
- Received by editor(s): November 6, 2009
- Published electronically: April 28, 2010
- Additional Notes: We thank Kevin Pilgrim for piquing our interest in realizing Lattès maps as subdivision maps of finite subdivision rules.
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn. 14 (2010), 113-140
- MSC (2010): Primary 37F10, 52C20; Secondary 57M12
- DOI: https://doi.org/10.1090/S1088-4173-10-00203-1
- MathSciNet review: 2629972