# Iterations of rational functions: which hyperbolic components contain polynomials?

@inproceedings{Przytycki1994IterationsOR, title={Iterations of rational functions: which hyperbolic components contain polynomials?}, author={Feliks Przytycki}, year={1994} }

Let $H^d$ be the set of all rational maps of degree $d\ge 2$ on the Riemann sphere which are expanding on Julia set. We prove that if $f\in H^d$ and all or all but one critical points (or values) are in the immediate basin of 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 immediate basin of attraction to an attracting fixed point or parabolic fixed point then $f$ restricted to Julia set is… CONTINUE READING

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