We propose a condition called no energy gap for a flow on a
C$^*$-algebra, which is expressed in terms of spectral subspaces,
and find an equivalent condition on the primitive ideals of the
crossed product which says that any primitive ideal is monotonely
increasing or decreasing under the dual flow, when the C$^*$-algebra
is simple and the flow is outer. We also discuss some examples
involving UHF flows.
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