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This article is cited in 15 scientific papers (total in 15 papers)
On the 75th birthday of Professor L.P. Shilnikov
Rigorous and accurate enclosure of invariant manifolds on surfaces
A. Wittiga, M. Berza, J. Grotea, K. Makinoa, S. Newhouseb a Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA
b Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
Abstract:
Knowledge 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.
Keywords:
Taylor model, invariant manifold, hyperbolicity, homoclinic point.
Received: 20.12.2009 Accepted: 14.01.2010
Citation:
A. Wittig, M. Berz, J. Grote, K. Makino, S. Newhouse, “Rigorous and accurate enclosure of invariant manifolds on surfaces”, Regul. Chaotic Dyn., 15:2-3 (2010), 107–126
Linking options:
https://www.mathnet.ru/eng/rcd482 https://www.mathnet.ru/eng/rcd/v15/i2/p107
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