Poincaré functions with spiders' webs

Details Poincaré functions with spiders' webs Poincaré functions with spiders' webs

2010-10-02

arxiv.org/abs/1010.0299v1

Proc. Amer. Math. Soc. 2012

Mathematics

Dynamical Systems

15 pages

Scientific paper

10.1090/S0002-9939-2012-11164-5

For a polynomial p with a repelling fixed point w, we consider Poincar\'{e} functions of p at w, i.e. entire functions L which satisfy L(0)=w and p(L(z))=L(p'(w)*z) for all z in the complex plane. We show that if the component of the Julia set of p that contains w equals {w}, then the (fast) escaping set of L is a spider's web; in particular it is connected. More precisely, we classify all linearizers of polynomials with regards to the spider's web structure of the set of all points which escape faster than the iterates of the maximum modulus function at a sufficiently large point.

Affiliated with

Also associated with

No associations

Rating

Poincaré functions with spiders' webs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Poincaré functions with spiders' webs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Poincaré functions with spiders' webs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-519387