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}
}
  • Feliks Przytycki
  • Published 1994
  • Mathematics
  • 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