Rigorous and Accurate Enclosure of Invariant Manifolds on Surfaces
AbstractKnowledge about stable and unstable manifolds of hyperbolic
fixed points of certain maps is desirable in many fields of research, both in
pure mathematics as well as in applications, ranging from forced oscillations
to celestial mechanics and space mission design. We present a technique to
find highly accurate polynomial approximations of local invariant manifolds
for sufficiently smooth planar maps and rigorously enclose them with sharp
interval remainder bounds using Taylor model techniques. Iteratively, significant
portions of the global manifold tangle can be enclosed with high accuracy.
Numerical examples are provided.
A. Wittig, M. Berz, J. Grote, K. Makino, S. Newhouse,
Regular and Chaotic Dynamics 15,2-3 (2010) 107-126
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