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@article{Cheraghi:2019,
author = {Cheraghi, D},
journal = {Annales Scientifiques de l'Ecole Normale Superieure},
pages = {59--138},
title = {Typical orbits of quadratic polynomials with a neutral fixed point I: non-Brjuno type},
url = {https://smf.emath.fr/publications/orbites-typiques-des-polynomes-quadratiques-avec-un-point-fixe-neutre-type-non-brjuno},
volume = {52},
year = {2019}
}

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TY  - JOUR
AB  - We study (Lebesgue) typical orbits of quadratic polynomials $P_a(z)=e^{2\pia} z+z^2: C -> C$, with $a$ of non-Brjuno and high return type. This includesquadratic polynomials with positive area Julia set of X. Buff and A. Cheratat.As a consequence, we introduce rational maps of arbitrarily large degree forwhich the Brjuno condition is optimal for their linearizability. Our techniqueuses the near-parabolic renormalization developed by H. Inou and M. Shishikura.
AU  - Cheraghi,D
EP  - 138
PY  - 2019///
SN  - 0012-9593
SP  - 59
TI  - Typical orbits of quadratic polynomials with a neutral fixed point I: non-Brjuno type
T2  - Annales Scientifiques de l'Ecole Normale Superieure
UR  - https://smf.emath.fr/publications/orbites-typiques-des-polynomes-quadratiques-avec-un-point-fixe-neutre-type-non-brjuno
UR  - http://hdl.handle.net/10044/1/53674
VL  - 52
ER  -

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