AN IMPROVEMENT OF J: RIVERA-LETELIER RESULT ON WEAK HYPERBOLICITY ON PERIODIC ORBITS FOR POLYNOMIALS
We prove that for f : <img border=0 width=50 height=19 id="_x0000_i1026" src="http:/fbpe/img/proy/v24n3/img06-01.jpg">a rational mapping of the Riemann sphere of degree at least 2 and W a simply connected immediate basin of attraction to an attracting fixed point, if |(f n)...
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| Autor principal: | |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2005
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| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172005000300006 |
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| Sumario: | We prove that for f : <img border=0 width=50 height=19 id="_x0000_i1026" src="http:/fbpe/img/proy/v24n3/img06-01.jpg">a rational mapping of the Riemann sphere of degree at least 2 and W a simply connected immediate basin of attraction to an attracting fixed point, if |(f n)'(p)| ³ Cn³+x for constants x > 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 : <img border=0 width=50 height=18 id="_x0000_i1027" src="http:/fbpe/img/proy/v24n3/img06-02.jpg">extends continuously to <img border=0 width=20 height=18 id="_x0000_i1028" src="http:/fbpe/img/proy/v24n3/img06-03.jpg">and FrW is locally connected. This improves a result proved by J. Rivera-Letelier for W the basin of infinity for polynomials, and 5 + x rather than 3 + x. |
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