  It is shown that the initial compression in central heavy ion collisions at
beam energies of $E_\mathrm{lab}=1-10A$~GeV depends dominantly on the
underlying equation of state and only marginally on the model used for the
dynamical description. To do so, a procedure to incorporate any equation of
state in the UrQMD transport model is introduced. In particular we compare the
baryon density, temperature and pressure evolution as well as produced entropy
in a relativistic ideal hydrodynamics approach and the UrQMD transport model,
where the same equation of state is used in both approaches. Not only is the
compression similar if the same equation of state is used in either dynamical
model, but it also strongly depends on the actual equation of state. These
results indicate that the equation of state can be studied with observables
which are sensitive to the initial compression phase and maximum compression
achieved in heavy ion collisions at these beam energies.
