@article{Przytycki_2017, title={An improvement of j. Rivera-letelier result on weak hyperbolicity on periodic orbits for polynomials}, volume={24}, url={https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1461}, DOI={10.4067/S0716-09172005000300006}, abstractNote={<p>We prove that for f :<img src="https://scielo.conicyt.cl/fbpe/img/proy/v24n3/img06-01.jpg" /> a rational mapping of the Riemann sphere of degree at least 2 and Ω a simply connected immediate basin of attraction to an attracting fixed point, if |(f <sup>n</sup>)’(p)| ≥ Cn<sup>3+ξ </sup> for constants ξ &gt; 0,C &gt; 0 all positive integers n and all repelling periodic points p of period n in Julia set for f, then a Riemann mapping R : <img src="https://scielo.conicyt.cl/fbpe/img/proy/v24n3/img06-02.jpg" /> extends continuously to <img src="https://scielo.conicyt.cl/fbpe/img/proy/v24n3/img06-03.jpg" /> and FrΩ is locally connected. This improves a result proved by J. Rivera-Letelier for Ω the basin of infinity for polynomials, and 5 + ξ rather than 3 + ξ.</p>}, number={3}, journal={Proyecciones (Antofagasta, On line)}, author={Przytycki, Feliks}, year={2017}, month={Apr.}, pages={277-286} }