Mathematics – Dynamical Systems
Scientific paper
2009-02-16
Duke Math. J. 154 (2010), 599-630
Mathematics
Dynamical Systems
21 pages
Scientific paper
For 0 < c < 1/e the Julia set of f(z) = c exp(z) is an uncountable union of pairwise disjoint simple curves tending to infinity [Devaney and Krych 1984], the Hausdorff dimension of this set is two [McMullen 1987], but the set of curves without endpoints has Hausdorff dimension one [Karpinska 1999]. We show that these results have three-dimensional analogues when the exponential function is replaced by a quasiregular self-map of three-space introduced by Zorich.
No associations
LandOfFree
Karpińska's paradox in dimension three 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 Karpińska's paradox in dimension three, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Karpińska's paradox in dimension three will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-463231