Show that the normal form of a nondegenerate Hopf singularity is given by

˙u

˙v

=

0 −β

β 0 u

v

+

au(u2 + v2) − bv(u2 + v2)

av(u2 + v2) + bu(u2 + v2)

+O(|u|5), whereβ > 0 and a = 0.