For dynamically convex star-shaped hypersurfaces in R^{2n}, at least floor((n+1)/2) geometrically distinct closed characteristics have irrational mean indices, and at least floor((n+1)/2)+1 have pairwise irrational mean-index ratios, provided the total number is finite.
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On the mean indices of closed characteristics on dynamically convex star-shaped hypersurfaces in $\mathbb{R}^{2n}$
For dynamically convex star-shaped hypersurfaces in R^{2n}, at least floor((n+1)/2) geometrically distinct closed characteristics have irrational mean indices, and at least floor((n+1)/2)+1 have pairwise irrational mean-index ratios, provided the total number is finite.