A geometric proof using blowup in complex phase space shows that manifold splitting in the generic zero-Hopf bifurcation of codimension two is exponentially small due to non-analytic center-like manifolds.
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A geometric approach to exponentially small splitting: The generic zero-Hopf bifurcation of co-dimension two
A geometric proof using blowup in complex phase space shows that manifold splitting in the generic zero-Hopf bifurcation of codimension two is exponentially small due to non-analytic center-like manifolds.