  We investigate the evolution of a single qubit subject to a continuous
unitary dynamics and an additional interrupting influence which occurs
periodically. One may imagine a dynamically evolving closed quantum system
which becomes open at certain times. The interrupting influence is represented
by an operation, which is assumed to equivalently describe a non-selective
unsharp measurement. It may be decomposed into a positive operator, which in
case of a measurement represents the pure measurement part, followed by an
unitary back-action operator. Equations of motion for the state evolution are
derived in the form of difference equations. It is shown that the 'free'
Hamiltonian is completed by an averaged Hamiltonian, which goes back to the
back-action. The positive operator specifies a decoherence rate and results in
a decoherence term. The continuum limit to a master equation is performed. The
selective evolution is discussed and correcting higher order terms are worked
out in an Appendix.
