Question: Problem 8.2. Suppose L C 1 (M, R). Let VR = {x M|L(x) R} be a compact set and suppose the Lie derivative satisfies grad(L)(x)

Problem 8.2. Suppose L C 1 (M, R). Let VR = {x M|L(x) R} be a compact set and suppose the Lie derivative satisfies grad(L)(x) f(x) < 0, x : L(x) = R. Then every connected component of VR is a trapping region.

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