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Common zeroes of families of smooth vector fields on surfaces

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 نشر من قبل Morris Hirsch
 تاريخ النشر 2015
  مجال البحث
والبحث باللغة English
 تأليف Morris W. Hirsch




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Let Y and X denote C^k vector fields on a possibly noncompact surface with empty boundary, k >0. Say that Y tracks X if the dynamical system it generates locally permutes integral curves of X. Let K be a locally maximal compact set of zeroes of X. THEOREM Assume the Poincare-Hopf index of X at K is nonzero, and the k-jet of X at each point of K is nontrivial. If g is a supersolvable Lie algebra of C^k vector fields that track X, then the elements of g have a common zero in K. Applications are made to attractors and transformation groups.



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