Iterative square roots of functions

Article Type

Research Article

Publication Title

Ergodic Theory and Dynamical Systems

Abstract

An iterative square root of a self-map f is a self-map g such that. We obtain new characterizations for detecting the non-existence of such square roots for self-maps on arbitrary sets. They are used to prove that continuous self-maps with no square roots are dense in the space of all continuous self-maps for various topological spaces. The spaces studied include those that are homeomorphic to the unit cube in and to the whole of for every positive integer However, we also prove that every continuous self-map on a space homeomorphic to the unit cube in with a fixed point on the boundary can be approximated by iterative squares of continuous self-maps.

First Page

2201

Last Page

2227

DOI

https://10.1017/etds.2022.35

Publication Date

7-24-2023

Comments

Open Access, Green

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