Preprint of the project:
95-012 Wolf-Jürgen Beyn, Jan-Martin Kleinkauf.
The Numerical Computation of Homoclinic Orbits for Maps
Transversal homoclinic orbits of maps
are known to generate shift dynamics on a set with Cantor like
structure. In this paper a numerical method is developed for
computation of the corresponding homoclinic orbits. They are
approximated by finite orbit segments subject to asymptotic
boundary conditions. We provide a detailed error analysis
including a shadowing type result by which one can infer the
existence of a transversal homoclinic orbit from a finite
segment. This approach is applied to several examples. In some
of them parameters appear and closed loops of homoclinic orbits
are found by a path-following algorithm.
