Combinatorial rigidity for some infinitely renormalizable unicritical polynomials
File(s)Conformal Geometry and Dynamics_14_2010.pdf (651.96 KB)
Published version
Author(s)
Cheraghi, D
Type
Journal Article
Abstract
We prove combinatorial rigidity of infinitely renormalizable unicritical
polynomials, P_c :z \mapsto z^d+c, with complex c, under the a priori bounds
and a certain "combinatorial condition". This implies the local connectivity of
the connectedness loci (the Mandelbrot set when d = 2) at the corresponding
parameters.
polynomials, P_c :z \mapsto z^d+c, with complex c, under the a priori bounds
and a certain "combinatorial condition". This implies the local connectivity of
the connectedness loci (the Mandelbrot set when d = 2) at the corresponding
parameters.
Date Issued
2010-09-15
Citation
CONFORMAL GEOMETRY AND DYNAMICS, An Electronic Journal of the American Mathematical Society, 2010, 14, pp.219-255
ISSN
1088-4173
Publisher
American Mathematical Society
Start Page
219
End Page
255
Journal / Book Title
CONFORMAL GEOMETRY AND DYNAMICS, An Electronic Journal of the American Mathematical Society
Volume
14
Copyright Statement
© Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - See more at: http://www.ams.org/journals/ecgd/2010-14-13/S1088-4173-2010-00216-X/home.html#sthash.ppyC8lFF.dpuf
The copyright for this article reverts to public domain 28 years after publication. - See more at: http://www.ams.org/journals/ecgd/2010-14-13/S1088-4173-2010-00216-X/home.html#sthash.ppyC8lFF.dpuf
Identifier
http://www.ams.org/journals/ecgd/2010-14-13/S1088-4173-2010-00216-X/S1088-4173-2010-00216-X.pdf
Publication Status
Published
Publisher URL
Coverage Spatial
USA