  We will give an example of a smooth free action of $S^1=U(1)$ on $S^7$ whose
orbits have unbounded lenghts (equivalently: unbounded periods). As an
application of this example we construct a $C^{\infty}$ vector field $X$,
defined in a neighbourhood $U$ of $0 \in \mathbb{R}^8$, such that: $U-\{0\}$ is
foliated by closed integral curves of $X$, the differential $DX(0)$ at $0$
defines a $1$-parameter group of nondegenerate rotations and $X$ is {\it not}
orbitally equivalent to its linearization. This proves in the $C^{\infty}$
category that the classical Poincar\'e Centre Theorem, true for planar
nondegenerate centres, is not generalizable to multicentres.
