An improvement of j. Rivera-letelier result on weak hyperbolicity on periodic orbits for polynomials

• Przytycki, Feliks ^[1]
  1. [1] Polish Academy of Sciences

     Polish Academy of Sciences

     Warszawa, Polonia

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 24, Nº. 3, 2005, págs. 277-286
• Idioma: inglés
• DOI: 10.4067/S0716-09172005000300006
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• Resumen

  • We prove that for f : ¯CI → ¯CI 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 n)0 (p)| ≥ Cn3+ξ for constants ξ > 0,C > 0 all positive integers n and all repelling periodic points p of period n in Julia set for f, then a Riemann mapping R : ID → Ω extends continuously to ¯ID 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.

• Referencias bibliográficas
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