The Linearization of the Equations of Motion
113
of the transfer map
(x|xx) = k
1
3
sin
2 s −
1
3
cos s +
1
3
,
(x|xa) = k
−
2
3
sin s cos s +
2
3
sin s
,
(x|aa) = k
1
3
cos
2 s −
2
3
cos s +
1
3
,
(a|xx) = k
2
3
sin s cos s +
1
3
sin s
,
(a|xa) = k
2
3
sin
2 s −
2
3
cos
2 s +
2
3
cos s
,
(a|aa) = k
−
2
3
sin s cos s +
2
3
sin s
.
In a similar fashion, but with much more effort, one can also compute the
third and higher order terms.