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تسجيل مستخدم جديدZero sets of Abelian Lie algebras of vector fields
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تأليف
Morris W. Hirsch
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Assume M is a 3-dimensional real manifold without boundary, A is an abelian Lie algebra of analytic vector fields on M, and X is an element of A. The following result is proved: If K is a locally maximal compact set of zeroes of X and the Poincare-Hopf index of X at K is nonzero, there is a point in K at which all the elements of A vanish.
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Let X be an analytic vector field on a real or complex 2-manifold, and K a compact set of zeros of X whose fixed point index is not zero. Let A denote the Lie algebra of analytic vector fields Y on M such that at every point of M the values of X and
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