Hausdorff dimensions of escaping sets of transcendental entire functions

Details Hausdorff dimensions of escaping sets of transcendental entire functions Hausdorff dimensions of escaping sets of transcendental entire functions

2009-04-20

arxiv.org/abs/0904.3072v1

Proc. Amer. Math. Soc. 138 (2010), 1657-1665.

Mathematics

Dynamical Systems

9 pages

Scientific paper

10.1090/S0002-9939-09-10104-1

Let $f$ and $g$ be transcendental entire functions, each with a bounded set of singular values, and suppose that $f$ and $g$ are affinely equivalent (that is, $g \circ \phi= \psi\circ f$, where $\phi,\psi:\C\to\C$ are affine). We show that the escaping sets of $f$ and $g$ have the same Hausdorff dimension. Using a result of the second author, we deduce that there exists a family of transcendental entire functions for which the escaping set has Hausdorff dimension equal to one.

Affiliated with

Also associated with

No associations

Rating

Hausdorff dimensions of escaping sets of transcendental entire functions 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 Hausdorff dimensions of escaping sets of transcendental entire functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hausdorff dimensions of escaping sets of transcendental entire functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-174407