Numerical analysis of high-dimensional
transfer operators
06-029 Thorsten Hüls.
Homoclinic Orbits of Non-Autonomous Maps and
their Approximation
We consider homoclinic orbits in non-autonomous discrete time
dynamical systems of the form
xn+1 = fn(xn), n ∈ Z,
where it is assumed that an n independent fixed point exists. A
numerical method for computing finite approximations of transversal
homoclinic orbits is introduced and a detailed error analysis is
presented. The non-autonomous setup requires special tools. We prove
that the analytic condition of transversality of the orbit
corresponds to a transversal intersection of the corresponding
invariant fiber bundles. The approximation method
and the validity of the error estimate
is illustrated by an
example.
