  We study the initial value problem '$s\,' = c^{p - 1}, \; c\,' = -s^{p - 1};
\; \; s(0) = 0, \; c(0) = 1$' (both as a real system and as a complex system)
for each integer $p > 2$, considering separately the cases '$p$ even' and '$p$
odd'.
