A little experimentation shows that if we sum the series (5) up to and
including n=5, then 
circles suffice for analytical continuation
from t = 0 to t = 1, the period of the drive. The coefficients 
, for arbitrary A, are sufficiently simple algebraic expressions to
be included in the Appendix. We now compare the ¶ map constructed in the way
described with numerical calculations. The latter were carried out using
a variable-order, variable step routine from the NAG library,
with a tolerance 
.