Stable intersections of Cantor sets and homoclinic bifurcations
Hausdorff measures and the Morse-Sard theorem.
Let F : U ⊂ R → R be a differentiable function and p < m an integer. If k ≥ 1 is an integer, α ∈ [0, 1] and F ∈ C, if we set C(F) = {x ∈ U | rank(Df(x)) ≤ p} then the Hausdorff measure of dimension (p + (n-p)/(k+α)) of F(C(F)) is zero.
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