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Orbits of Maps
Forward orbits of maps are generated in the same
manner as generating the forward orbit of a
flow. Position the pointer within
the 2-D Image window; click
to
set an initial point and
to iterate
the map forward.
Continue the iteration with
.
You can also use the Orbits
and Selected Point panels as with vector fields.
You will
see that for the default parameter values
almost every initial condition is
mapped asymptotically towards an invariant
curve which winds around the torus.
Since this map is a diffeomorphism (for small
values of the nonlinearity a), the inverse
of the map exists, and therefore we can compute
backward orbits. Click
followed by
a few times and convince yourself that almost every
initial condition is backwards asymptotic to a period
five orbit for the default parameter values. (Figure
)
root
1998-11-02