On the distality and expansivity of certain maps on spheres
Manoj Choudhuri, Gianluca Faraco, and Alok Kumar Yadav

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.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Advanced Mathematical Theories and Applications
