Do close flows which are far from the identity have close vector fields?
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From: LordBeotian on 9 May 2010 13:34 Suppose I have two vector fields v and w such that 1) |v|>a, |w|>a 2) v_t and w_t are the corresponding flow and |w_1-v_1|<b is it true that assuming 1 and 2 we have |v-w|<C*b/a ? The only way I see to prove this is to consider the vector field as the fixed point of the relation v(v_1(x))=Dv_1(x)v_1(x) but this would involve an implicit function theorem in infinite dimension... Any advise? |