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October, 2001 Non-linearizability of n-subhyperbolic polynomials at irrationally indifferent fixed points
J. Math. Soc. Japan 53(4): 847-874 (October, 2001). DOI: 10.2969/jmsj/05340847


We study the non-linearlizability conjecture (NLC) for polynomials at non-Brjuno irrationally indifferent fixed points. A polynomial is n-subhyperbolic if it has exactly n recurrent critical points corresponding to irrationally indifferent cycles, other ones in the Julia set are preperiodic and no critical orbit in the Fatou set accumulates to the Julia set. In this article, we show that NLC and, more generally, the cycle-version of NLC are true in a subclass of n-subhyperbolic polynomials. As a corollary, we prove the cycle-version of the Yoccoz Theorem for quadratic polynomials.

We also study several specific examples of n-subhyperbolic polynomials. Here we also show the scaling invariance of the Brjuno condition: if an irrational number α satisfies the Brjuno condition, then so do mα for every positive integer m.


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Yûsuke OKUYAMA. "Non-linearizability of n-subhyperbolic polynomials at irrationally indifferent fixed points." J. Math. Soc. Japan 53 (4) 847 - 874, October, 2001.


Published: October, 2001
First available in Project Euclid: 29 May 2008

zbMATH: 1030.37032
MathSciNet: MR1852886
Digital Object Identifier: 10.2969/jmsj/05340847

Primary: 37F50
Secondary: 30D05 , 37F10 , 37F25 , 37F30

Keywords: $n$-subhyperbolic polynomiaj quadratic polynomiaj irrationally indifferent cycle , Brjuno condition , non-linearizability , renormalization , Teichm{\"u}ller space

Rights: Copyright © 2001 Mathematical Society of Japan


Vol.53 • No. 4 • October, 2001
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