Typical orbits of quadratic polynomials with a neutral fixed point I: non-Brjuno type

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Title: Typical orbits of quadratic polynomials with a neutral fixed point I: non-Brjuno type
Authors: Cheraghi, D
Item 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.
Issue Date: 12-Jul-2016
URI: http://hdl.handle.net/10044/1/53674
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/M01746X/1
Keywords: math.DS
math.CV
37F50, 46T25, 37F25
0105 Mathematical Physics
0206 Quantum Physics
0101 Pure Mathematics
Mathematical Physics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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