If at a point
the the point
is said to be a fixed point, labelled
and
for any motion which starts at a fixed point.One example is shown above,
This motion has three fixed points, at
These points may be classified as stable, or unstable.
The function
may be expanded in a Taylor series about a fixed pointto give
with solution
where
If
thentends to
for any particle with initial position
since
and if
tends tosince