Strong bifurcation loci of full Hausdorff dimension

Details Strong bifurcation loci of full Hausdorff dimension Strong bifurcation loci of full Hausdorff dimension

2011-03-14

arxiv.org/abs/1103.2656v3

Mathematics

Dynamical Systems

37 pages

Scientific paper

In the moduli space $\mathcal{M}_d$ of degree $d$ rational maps, the bifurcation locus is the support of a closed $(1,1)$ positive current $T_\bif$ which is called the bifurcation current. This current gives rise to a measure $\mu_\bif:=(T_\bif)^{2d-2}$ whose support is the seat of strong bifurcations. Our main result says that $\supp(\mu_\bif)$ has maximal Hausdorff dimension $2(2d-2)$. As a consequence, the set of degree $d$ rational maps having $2d-2$ distinct neutral cycles is dense in a set of full Hausdorff dimension.

Affiliated with

Also associated with

No associations

Rating

Strong bifurcation loci of full Hausdorff dimension 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 Strong bifurcation loci of full Hausdorff dimension, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Strong bifurcation loci of full Hausdorff dimension will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-259560