Dynamics of a higher dimensional analog of the trigonometric functions
Dynamical Systems
2012-04-16 v1 Complex Variables
Abstract
We introduce a higher dimensional quasiregular map analogous to the trigonometric functions and we use the dynamics of this map to define, for d>1, a partition of d-dimensional Euclidean space into curves tending to infinity such that two curves may intersect only in their endpoints and such that the union of the curves without their endpoints has Hausdorff dimension one.
Keywords
Cite
@article{arxiv.1002.4159,
title = {Dynamics of a higher dimensional analog of the trigonometric functions},
author = {Walter Bergweiler and Alexandre Eremenko},
journal= {arXiv preprint arXiv:1002.4159},
year = {2012}
}
Comments
12 pages