The coherent effects implied by the magnetic field jump [B> and the deHoffmann-Teller frame (HTF) potential jump [&PHgr;HT> on electron heating and phase space signatures at shocks of different strengths are presented. Of particular interest is whether these coherent effects have sufficiently different signatures to explain the observed preferential transverse heating in weak shocks while still producing nearly isotropic heating for strong shocks. Vlasov-Liouville mappings of an upstream electron core-halo distribution function f1, modified to reflect electron mirroring, are employed to determine the downstream electron distribution function f2. Electrons within the shock are treated as a laminar Vlasov guiding center ordered fluid. These mappings demonstrate that the coherent effects play a major role in producing, at all pitch angles, characteristic electron distribution function signatures observed behind strong and weak shocks and thus significantly impact electron heating. A favorable test of the Vlasov-Liouville mapping concept was performed using detailed upstream and downstream distribution functions at a weak bow shock observed by Galileo on the second Earth flyby. Especially noteworthy is that the Vlasov-Liouville procedure recovers the anisotropic inflationary signatures of the observed downstream electron distribution function. ¿ 1998 American Geophysical Union