  We have measured Hall effect, magnetotransport and magnetostriction on the
field induced phases of single crystalline UPt$_2$Si$_2$ in magnetic fields up
to 60\,T at temperatures down to 50\,mK. For the magnetic field applied along
the $c$ axis we observe strong changes in the Hall effect at the phase
boundaries. From a comparison to band structure calculations utilizing the
concept of a dual nature of the uranium 5$f$ electrons, we find evidence for
field induced topological changes of the Fermi surface due to at least one
Lifshitz transition. Furthermore, we find a unique history dependence of the
magnetotransport and magnetostriction data, indicating that the Lifshitz type
transition is of a discontinuous nature, as predicted for interacting electron
systems.
