A brief outline of the longitudinal single particle dynamics at transition is presented in terms of phase‐space mappings. Simple qunatitative prediction about the phase‐space dilution is made. More realistic simulation (ESME) of the transition crossing is carried out (including various collective and single particle effects contributing to the longitudinal emittance blow up). The simulation takes into account the longitudinal space‐charge force (bunch length oscillation), the transverse space‐charge (the Umsta¨tter effect) and finally the dispersion of the momentum compaction factor (the Johnsen effect). As a result of this simulation one can separate relative strengths of the above mechanisms and study their individual effects on the longitudinal phase‐space evolution, espcially filamentation of the bunch and formation of a ‘‘galaxy‐like’’ pattern.