Blocks of monodromy groups in Complex Dynamics

Details Blocks of monodromy groups in Complex Dynamics Blocks of monodromy groups in Complex Dynamics

2009-01-28

arxiv.org/abs/0901.4526v2

Mathematics

Dynamical Systems

15 pages, 4 figures

Scientific paper

Motivated by a problem in complex dynamics, we examine the block structure of the natural action of monodromy groups on the tree of preimages of a generic point. We show that in many cases, including when the polynomial has prime power degree, there are no large blocks other than those arising naturally from the tree structure. However, using a method of construction based on real graphs of polynomials, we exhibit a non-trivial example of a degree 6 polynomial failing to have this property. This example settles a problem raised in a recent paper of the second author regarding constant weighted sums of polynomials in the complex plane. We also show that degree 6 is exceptional in another regard, as it is the lowest degree for which the monodromy group of a polynomial is not determined by the combinatorics of the post-critical set. These results give new applications of iterated monodromy groups to complex dynamics.

Affiliated with

Also associated with

No associations

Rating

Blocks of monodromy groups in Complex Dynamics 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 Blocks of monodromy groups in Complex Dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Blocks of monodromy groups in Complex Dynamics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-345313