Typical orbits of quadratic polynomials with a neutral fixed point I: non-Brjuno type
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Accepted version
Author(s)
Cheraghi, D
Type
Working Paper
Abstract
We study (Lebesgue) typical orbits of quadratic polynomials $P_a(z)=e^{2\pi
a} z+z^2: C -> C$, with $a$ of non-Brjuno and high return type. This includes
quadratic polynomials with positive area Julia set of X. Buff and A. Cheratat.
As a consequence, we introduce rational maps of arbitrarily large degree for
which the Brjuno condition is optimal for their linearizability. Our technique
uses the near-parabolic renormalization developed by H. Inou and M. Shishikura.
a} z+z^2: C -> C$, with $a$ of non-Brjuno and high return type. This includes
quadratic polynomials with positive area Julia set of X. Buff and A. Cheratat.
As a consequence, we introduce rational maps of arbitrarily large degree for
which the Brjuno condition is optimal for their linearizability. Our technique
uses the near-parabolic renormalization developed by H. Inou and M. Shishikura.
Date Issued
2019-01-01
Date Acceptance
2016-01-01
Citation
Annales Scientifiques de l'Ecole Normale Superieure, 2019, 52 (1), pp.59-138
ISSN
0012-9593
Publisher
SMF
Start Page
59
End Page
138
Journal / Book Title
Annales Scientifiques de l'Ecole Normale Superieure
Volume
52
Issue
1
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Identifier
https://smf.emath.fr/publications/orbites-typiques-des-polynomes-quadratiques-avec-un-point-fixe-neutre-type-non-brjuno
Grant Number
EP/M01746X/1
Subjects
math.DS
math.CV
37F50, 46T25, 37F25
0105 Mathematical Physics
0206 Quantum Physics
0101 Pure Mathematics
Mathematical Physics
Publication Status
Published