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Integrality and rigidity for postcritically finite polynomials

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Epstein, Adam L.. (2012) Integrality and rigidity for postcritically finite polynomials. Bulletin of the London Mathematical Society, Vol.44 (No.1). pp. 39-46. ISSN 0024-6093

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Official URL: http://dx.doi.org/10.1112/blms/bdr059

Abstract

We give an arithmetic proof of rigidity for postcritically finite polynomials of prime power degree.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Polynomials, Rigidity (Geometry)
Journal or Publication Title:	Bulletin of the London Mathematical Society
Publisher:	Cambridge University Press
ISSN:	0024-6093
Date:	February 2012
Volume:	Vol.44
Number:	No.1
Number of Pages:	8
Page Range:	pp. 39-46
Identification Number:	10.1112/blms/bdr059
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
References:	[1] J. Bobenrieth, The multiplier map on hyperbolic components of a family of rational maps, 2000 manuscript. [2] B. Branner & J. H. Hubbard, The iteration of cubic polynomials. Part I: The global topology of parameter space, Acta. Math. 160 (1988), 143- 206. [3] X. Buff, A. Epstein, S. Koch & K. Pilgrim, On Thurston’s pullback map, in Complex dynamics, families and friends, ed. D. Schleicher, A. K. Peters, 2009. [4] A. Epstein, Transversality in holomorphic dynamics, 2010 manuscript, http://www.warwick.ac.uk/∼mases/Transversality.pdf. [5] A. Douady & J. H. Hubbard, Exploring the Mandelbrot set, The Orsay notes, http://www.math.cornell.edu/∼hubbard/OrsayEnglish.pdf. [6] A. Douady & J. H. Hubbard, A proof of Thurston’s topological characterization of rational functions, Acta Math. 171 (1993), 263-297. [7] A. Douady & J. H. Hubbard, On the dynamics of polynomial-like mappings, Ann. Sci. Ec. Norm. Sup. 4e Ser. 18 (1985), 287-344. [8] S. Lang, Algebraic number theory, Springer-Verlag, 1986. [9] J. Milnor, Hyperbolic components in spaces of polynomial maps, http://arxiv.org/abs/math/9202210. [10] J. Silverman, An algebraic approach to Thurston rigidity, 2010 manuscript. [11] J. Silverman, The arithmetic of dynamical systems, Springer-Verlag, 2007.
URI:	http://wrap.warwick.ac.uk/id/eprint/42157