  We compute the Hofer-Zehnder capacity of disk tangent bundles of certain lens
spaces with respect to the round metric. Interestingly we find that the
Hofer-Zehnder capacity does not see the covering, i.e. the capacity of the disk
tangent bundle of the lens space coincides with the capacity of the disk
tangent bundle of the 3-sphere covering it. In particular, this gives a first
example, where Gromov width and Hofer-Zehnder capacity of a disk tangent bundle
disagree. Techniques we use include for the lower bound magnetic billiards and
for the upper bound Gromov-Witten invariants.
