|
Lattès maps and finite subdivision rules
Author(s):
J.
W.
Cannon;
W.
J.
Floyd;
W.
R.
Parry
Journal:
Conform. Geom. Dyn.
14
(2010),
113-140.
MSC (2010):
Primary 37F10, 52C20;
Secondary 57M12
Posted:
April 28, 2010
MathSciNet review:
2629972
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
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:
-
- 1.
- M. Bonk and D. Meyer, Expanding Thurston maps, in preparation.
- 2.
- Z. I. Borevich and I. R. Shafarevich, Number Theory, Academic Press, New York and London, 1966. MR 0195803 (33:4001)
- 3.
- 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 (2007c:30048)
- 4.
- 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 (2008i:37093)
- 5.
- 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
- 6.
- A. Douady and J. H. Hubbard, A proof of Thurston's topological characterization of rational functions, Acta Math. 171 (1993), 263-297. MR 1251582 (94j:58143)
- 7.
- J. Milnor, Pasting together Julia sets: a worked out example of mating, Experimental Math. 13 (2004), 55-92. MR 2065568 (2005c:37087)
Similar Articles:
Retrieve articles in Conformal Geometry and Dynamics
with MSC
(2010):
37F10, 52C20,
57M12
Retrieve articles in all Journals with MSC
(2010):
37F10, 52C20,
57M12
Additional 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
Email:
floyd@math.vt.edu
W.
R.
Parry
Affiliation:
Department of Mathematics, Eastern Michigan University, Ypsilanti, Michigan 48197
Email:
walter.parry@emich.edu
DOI:
10.1090/S1088-4173-10-00203-1
PII:
S 1088-4173(10)00203-1
Keywords:
Finite subdivision rule,
Latt\`es map,
rational map,
conformality
Received by editor(s):
November 6, 2009
Posted:
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 of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
