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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| Lenguaje: | English |
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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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oai:scielo:S0716-091720050003000062006-03-10AN IMPROVEMENT OF J: RIVERA-LETELIER RESULT ON WEAK HYPERBOLICITY ON PERIODIC ORBITS FOR POLYNOMIALSPRZYTYCKI,FELIKSWe 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.24 n.3 20052005-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172005000300006en10.4067/S0716-09172005000300006 |
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Scielo Chile |
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Scielo Chile |
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English |
| description |
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. |
| author |
PRZYTYCKI,FELIKS |
| spellingShingle |
PRZYTYCKI,FELIKS AN IMPROVEMENT OF J: RIVERA-LETELIER RESULT ON WEAK HYPERBOLICITY ON PERIODIC ORBITS FOR POLYNOMIALS |
| author_facet |
PRZYTYCKI,FELIKS |
| author_sort |
PRZYTYCKI,FELIKS |
| title |
AN IMPROVEMENT OF J: RIVERA-LETELIER RESULT ON WEAK HYPERBOLICITY ON PERIODIC ORBITS FOR POLYNOMIALS |
| title_short |
AN IMPROVEMENT OF J: RIVERA-LETELIER RESULT ON WEAK HYPERBOLICITY ON PERIODIC ORBITS FOR POLYNOMIALS |
| title_full |
AN IMPROVEMENT OF J: RIVERA-LETELIER RESULT ON WEAK HYPERBOLICITY ON PERIODIC ORBITS FOR POLYNOMIALS |
| title_fullStr |
AN IMPROVEMENT OF J: RIVERA-LETELIER RESULT ON WEAK HYPERBOLICITY ON PERIODIC ORBITS FOR POLYNOMIALS |
| title_full_unstemmed |
AN IMPROVEMENT OF J: RIVERA-LETELIER RESULT ON WEAK HYPERBOLICITY ON PERIODIC ORBITS FOR POLYNOMIALS |
| title_sort |
improvement of j: rivera-letelier result on weak hyperbolicity on periodic orbits for polynomials |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2005 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172005000300006 |
| work_keys_str_mv |
AT przytyckifeliks animprovementofjriveraletelierresultonweakhyperbolicityonperiodicorbitsforpolynomials AT przytyckifeliks improvementofjriveraletelierresultonweakhyperbolicityonperiodicorbitsforpolynomials |
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