A note on iterated maps of the unit sphere

Authors

Chaitanya Gopalakrishna, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Aequationes Mathematicae

Abstract

Let C(S^m) denote the set of continuous maps from the unit sphere S^m in the Euclidean space R^m+1 into itself endowed with the supremum norm. We prove that the set {fⁿ:f∈C(S^m)andn≥2} of iterated maps is not dense in C(S^m). This, in particular, proves that the periodic points of the iteration operator of order n are not dense in C(S^m) for all n≥2, providing an alternative proof of the result that these operators are not Devaney chaotic on C(S^m) proved in Veerapazham et al. (Proc Am Math Soc 149(1):217–229, 2021).

First Page

503

Last Page

507

DOI

10.1007/s00010-023-00979-6

Publication Date

4-1-2024

Recommended Citation

Gopalakrishna, Chaitanya, "A note on iterated maps of the unit sphere" (2024). Journal Articles. 4553.
https://digitalcommons.isical.ac.in/journal-articles/4553