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Эта публикация цитируется в 15 научных статьях (всего в 15 статьях)
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
Аннотация:
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.
Ключевые слова:
Taylor model, invariant manifold, hyperbolicity, homoclinic point.
Поступила в редакцию: 20.12.2009 Принята в печать: 14.01.2010
Образец цитирования:
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
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd482 https://www.mathnet.ru/rus/rcd/v15/i2/p107
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