# 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

#### Citations

##### Publications citing this paper.
SHOWING 1-7 OF 7 CITATIONS

## On Connectivity of Fatou Components concerning a Family of Rational Maps

• Mathematics
• 2014

## Connectedness of Julia Sets of Rational Functions

• Mathematics
• 2001

## On Rational Maps with Two Critical Points

• John W. Milnor
• Mathematics, Computer Science
• Experimental Mathematics
• 1997

#### References

##### Publications referenced by this paper.
SHOWING 1-4 OF 4 REFERENCES

## On the iteration of a rational function: Computer experiments with Newton's method

• Mathematics
• 1983

## The mapping class group of a generic quadratic rational map and automorphisms of the 2-shift

• Mathematics
• 1990