A micromap approach to space charge is presented as a concept easily implemented in a computer code. A map of arbitrary length is found to be a suitable tool to include space charge by means of a kick approximation. We adopt space charge description where a transverse elliptic particle symmetry is assumed, and all analysis is carried out in a coasting beam approximation. This approach is particularly useful to investigate the single particle dynamics when the working point of a machine lies in a resonance driven by a skew quadrupole. Since the improvement of the multiturn injection efficiency due to linear coupling is based mainly on the exchange of emittance between x- and y-planes, we have investigated the emittance exchange dynamics when space charge is not negligible. We found that a coherent effect of space charge improves the efficiency of the exchange with respect to the case of single particle emittance exchange with space charge neglected. ©1998 American Institute of Physics.