Iterations of rational functions: which hyperbolic components contain polynomials?

Przytycki, Feliks

Fundamenta Mathematicae, Tome 149 (1996), p. 95-118 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $H^{d}$ be the set of all rational maps of degree d ≥ 2 on the Riemann sphere, expanding on their Julia set. We prove that if $f \in H^{d}$ and all, or all but one, critical points (or values) are in the basin of immediate attraction to an attracting fixed point then there exists a polynomial in the component H(f) of $H^{d}$ containing f. If all critical points are in the basin of immediate attraction to an attracting fixed point or a parabolic fixed point then f restricted to the Julia set is conjugate to the shift on the one-sided shift space of d symbols. We give exoticexamples of maps of an arbitrary degree d with a non-simply connected completely invariant basin of attraction and arbitrary number k ≥ 2 of critical points in the basin. For such a map $f \in H^{d}$ with k

Publié le : 1996-01-01

Zbl 0852.58052

EUDML-ID : urn:eudml:doc:212117

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     author = {Feliks Przytycki},
     title = {Iterations of rational functions: which hyperbolic components contain polynomials?},
     journal = {Fundamenta Mathematicae},
     volume = {149},
     year = {1996},
     pages = {95-118},
     zbl = {0852.58052},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv149i2p95bwm}
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Przytycki, Feliks. Iterations of rational functions: which hyperbolic components contain polynomials?. Fundamenta Mathematicae, Tome 149 (1996) pp. 95-118. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv149i2p95bwm/

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