On the distality and expansivity of certain maps on spheres

TL;DR

This paper investigates the dynamical properties, specifically distality and expansivity, of maps on spheres induced by affine transformations in Euclidean space, an area with limited prior research.

Contribution

It provides new insights into the dynamical behavior of sphere maps derived from affine transformations, focusing on properties like distality and expansivity.

Findings

Characterization of when these maps are distal

Conditions for expansivity of the maps

New results on the dynamical complexity of affine-induced sphere maps

Abstract

Any affine map on the (n+1)-dimensional Euclidean space gives rise to a natural map on the n-dimensional sphere whose dynamical aspects are not so well-studied in the literature. We explore the dynamical aspects of these maps by investigating about their distality and expansivity.