article · Indiana University Mathematics Journal · 2019
Linearizability of saturated polynomials
Cited by 7Open access
Abstract
Brjuno and R\"ussmann proved that every irrationally indifferent fixed point of an analytic function with a Brjuno rotation number is linearizable, and Yoccoz proved that this is sharp for quadratic polynomials. Douady conjectured that this is sharp for all rational functions of degree at least 2, i.e., that non-M\"obius rational functions cannot have Siegel disks with non-Brjuno rotation numbers. We prove that Douady's conjecture holds for the class of polynomials for which the number of infinite tails of critical orbits in the Julia set equals the number of irrationally indifferent cycles. As a corollary, Douady's conjecture holds for the polynomials $P(z) = z^d + c$ for all $d > 1$ and all complex $c$.
Cite this paper
Geyer, L. (2019). Linearizability of saturated polynomials. Indiana University Mathematics Journal, 68(5), 1551–1578. https://doi.org/10.1512/iumj.2019.68.6160
Geyer, Lukáš. “Linearizability of saturated polynomials.” Indiana University Mathematics Journal, vol. 68, no. 5, 2019, pp. 1551–78, https://doi.org/10.1512/iumj.2019.68.6160.
Geyer, Lukáš. 2019. “Linearizability of saturated polynomials.” Indiana University Mathematics Journal 68 (5): 1551–78. https://doi.org/10.1512/iumj.2019.68.6160.
Geyer, L. (2019) ‘Linearizability of saturated polynomials’, Indiana University Mathematics Journal, 68(5), pp. 1551–1578. Available at: https://doi.org/10.1512/iumj.2019.68.6160.
@article{geyer2019linearizability,
title = {{Linearizability of saturated polynomials}},
author = {Geyer, Lukáš},
journal = {Indiana University Mathematics Journal},
volume = {68},
number = {5},
pages = {1551--1578},
year = {2019},
doi = {10.1512/iumj.2019.68.6160}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.