Weak Hyperbolicity on Periodic Orbits for Polynomials

Details Weak Hyperbolicity on Periodic Orbits for Polynomials Weak Hyperbolicity on Periodic Orbits for Polynomials

2001-10-15

arxiv.org/abs/math/0110155v1

Mathematics

Dynamical Systems

6 pages, Latex

Scientific paper

We prove that if the multipliers of the repelling periodic orbits of a complex polynomial grow at least like $n^{5 + \epsilon}$, for some $\epsilon > 0$, then the Julia set of the polynomial is locally connected when it is connected. As a consequence for a polynomial the presence of a Cremer cycle implies the presence of a sequence of repelling periodic orbits with "small" multipliers. Somehow surprinsingly the proof is based in measure theorical considerations.

Affiliated with

Also associated with

No associations

Rating

Weak Hyperbolicity on Periodic Orbits for Polynomials 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 Weak Hyperbolicity on Periodic Orbits for Polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weak Hyperbolicity on Periodic Orbits for Polynomials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-622348