### 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.DSmath.CV37F50, 46T25, 37F250105 Mathematical Physics0206 Quantum Physics0101 Pure MathematicsMathematical Physics Publication Status: Published Appears in Collections: Pure MathematicsMathematicsFaculty of Natural Sciences

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