Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Rational maps with Fatou components of arbitrarily large connectivity (1704.00544v1)

Published 3 Apr 2017 in math.DS

Abstract: We study the family of singular perturbations of Blaschke products $B_{a,\lambda}(z)=z3\frac{z-a}{1-\overline{a}z}+\frac{\lambda}{z2}$. We analyse how the connectivity of the Fatou components varies as we move continuously the parameter $\lambda$. We prove that all possible escaping configurations of the critical point $c_-(a,\lambda)$ take place within the parameter space. In particular, we prove that there are maps $B_{a,\lambda}$ which have Fatou components of arbitrarily large finite connectivity within their dynamical planes.

Summary

We haven't generated a summary for this paper yet.