Abstract
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.
Funder
National Board for Higher Mathematics, India
J C Bose Fellowship, Science and Engineering Board, India
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
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