The nature of the spectrum depends on the interplay between the values of the actions. 
As said, choosing  carefully, one can choose the distance ; moreover, this can
be done in any compact subinterval of  of length at least 
On such an interval, the variations of the actions 
is at most of order 
Hence, we may essentially choose the parameters  arbitrarily and
independently of each other in their range of values.

For example, assume that . If  then, 
Theorem 5 and formula (3) imply that

Whereas, when  is only at a distance of size  (for ) from 
the set of energies , on , one has