The non-iterates are dense in the space of continuous self-maps

Article Type

Research Article

Publication Title

Nonlinearity

Abstract

In this paper we first prove a nonexistence result on iterative roots, which presents several sufficient conditions for identifying self-maps on arbitrary sets that have no iterative roots of any order. Then, using this result, we prove that when X is [ 0 , 1 ] m , R m or S 1 every non-empty open set of the space of continuous self-maps on X endowed with the compact-open topology contains a map that does not have even discontinuous iterative roots of order n ⩾ 2 . This, in particular, proves that the complement of , the set of non-iterates, is dense in for these X.

First Page

3419

Last Page

3430

DOI

https://10.1088/1361-6544/acd21f

Publication Date

6-1-2023

Comments

Open Access, Green

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