  In this article we study Rabinowitz Floer Homology for several interaction
particles. In general Rabinowitz action functional is invariant under
simultaneous time translation for all particles but not invariant if the times
of each particle are translated individually. The delayed Rabinowitz action
functional is invariant under individual time translation for each particle.
Although its critical point equation looks like a Hamiltonian delay equation it
is actually an ODE in disguise and nothing else than the critical point
equation of the undelayed Rabinowitz action functional. We show that we can
even interpolate between the two action functionals without changing the
critical points and their actions. Moreover, for each of these interpolating
action functionals we have compactness for gradient flow lines under a suitable
restricted contact type assumption.

Symplectic Geometry