Local Controllability and Semigroups of Diffeomorphisms
نویسنده
چکیده
1. I n t r o d u c t i o n 1. Let M be a real-analytic manifold, Vect M the Lie algebra of analytic vector fields on M. We consider a vector field f E Vect M as a differential operator of first order on the algebra of smooth functions C ~ (M) which satisfies the differentiation rule f(W1W2) -" (fw1)W2 + wI(fW2) VWI, W2 E Coo(M). A point z E M will be identified with the corresponding homomorphism z: Coo(M) ~ I~, ~ ~ ~(z). A tangent vector ~ E T~M is a linear functional ~: Coo(M) ---* I~ which satisfies condition
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