The class of concentrated periodic diffeomorphisms
g
:
M
→
M
g:M \to M
is introduced. A diffeomorphism is called concentrated if, roughly speaking, its normal eigenvalues range in a small (with respect to the period of
g
g
and the dimension of
M
M
) arc on the circle. In many ways, the cyclic action generated by such a
g
g
behaves on the one hand as a circle action and on the other hand as a generic prime power order cyclic action. For example, as for circle actions,
Sign
(
g
,
M
)
=
Sign
(
M
g
)
\operatorname {Sign} (g,M) = \operatorname {Sign} ({M^g})
, provided that the left-hand side is an integer; as for prime power order actions,
g
g
cannot have a single fixed point if
M
M
is closed. A variety of integrality results, relating to the usual signatures of certain characteristic submanifolds of the regular neighbourhood of
M
g
{M^g}
in
M
M
to
Sign
(
g
,
M
)
\operatorname {Sign} (g,M)
via the normal
g
g
-representations, is established.