Dynamics of a higher dimensional analog of the trigonometric functions

TL;DR

This paper introduces a higher-dimensional quasiregular map similar to trigonometric functions and studies its dynamics to partition space into curves with specific intersection and dimensional properties.

Contribution

It presents a novel higher-dimensional analog of trigonometric functions using quasiregular maps and analyzes their dynamic properties to create a unique space partition.

Findings

Partition of space into curves tending to infinity

Curves intersect only at endpoints

Union of curves has Hausdorff dimension one

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.