ABSTRACT. To every positive C-quadratic differential form defined on an oriented two manifold is associated a pair of transversal one-dimensional Cfoliations with common singularities.An open set of positive C-quadratic differential forms with structural stable associated foliations is characterized and it is proved that this set is dense in the space of positive C°°-quadratic differential forms with C2-topology. Also a realization theorem is established.
We consider sufficient conditions which guarantee that an embedding from the plane R 2 into itself has a unique fixed point. We study sufficient conditions which imply the appearing of a globally attracting fixed point for such an embedding.
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