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Observe that for any y ∈ K +, we have ind ( K, y ) = 1 or 2, thus from (16), y cannot be dominated through the flow lines of ( − ∂ K ) only by critical points y ′ of K such that ind ( K, y ′ ) = 2, thus it satisfies − Δ K ( y ′ ) > 0. Therefore we obtain W s ( y ) ∩ W u ( z ) = ∅, ∀ z ∈ K ∖ K +.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com