A classification of bicritical rational maps with a pair of period two superattracting cycles

Adam Epstein; Thomas Sharland

Displaying similar documents to “A classification of bicritical rational maps with a pair of period two superattracting cycles”

Iterations of rational functions: which hyperbolic components contain polynomials?

Feliks Przytycki (1996)

Fundamenta Mathematicae

Similarity:

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...