lie_derivative.pdf
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Math230a (Fall 2025) Yum-Tong Siu 1 Lie Derivative §1. Integral Function of Smooth Vector Field Let ⃗v = (v 1 , · · · , v k ) be a C k vector field (where k ∈ [0, ∞] is chosen so that the regularity conditions required by the arguments presented here are satisfied) on an open neighborhood U of 0 in Rn . To avoid the introduction of more notations, we agree to shrink U if necessary without changing the notation U . There exists some η > 0 such that for a = (a1 , · · · , an ) with |a| < η the ordinary…
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