Generalized bifurcation of higher dimensional tori |
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Authors: | Dietrich Flockerzi |
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Affiliation: | Mathematisches Institut, Universität Würzburg, Am Hubland, D-8700 Würzburg, West Germany |
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Abstract: | From the structural stability viewpoint vector fields on M which are tangent to the boundary of M are analysed. A class of vector fields is characterized as structurally stable; this class corresponds to the class of Morse-Smale vector fields on closed manifolds, studied by Palis, Peixoto Smale, and others. In this class, new phenomena occur as saddle connections along the boundary of M which are persistent by small perturbations. Thus, the techniques introduced by J. Palis (Topology8 (1969)), which inspired the proof of the stability of a vector field in such a class, were substantially changed. Such modifications represent a main difficulty in extending our results to higher dimensions. |
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