  We construct non-compact contact manifolds containing compact Legendrians
which can be displaced from their Reeb flow with arbitrarily small oscillation
energy. We use this to show the Shelukhin-Chekanov-Hofer pseudo-metric
considered by Rosen and Zhang is degenerate on the isotopy class of the
constructed Legendrians. Other aspects related to oscillation energy of
Legendrian isotopies are explored.
