Abstract
In this paper, let n ⩾ 2 be an integer, P = diag(-I n-κ I κ , -I n-κ ,I κ ) for some integer κ ∈ [0, n), and Σ ⊂ ℝ2n be a partially symmetric compact convex hypersurface, i.e., x ∈ Σ implies Px ∈ Σ. We prove that if Σ is (r, R)-pinched with \(\tfrac{R} {r} < \sqrt 2 \), then there exist at least n − κ geometrically distinct P-symmetric closed characteristics on Σ, as a consequence, Σ carry at least n geometrically distinct P-invariant closed characteristics.
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Liu, H., Zhang, D. On the number of P-invariant closed characteristics on partially symmetric compact convex hypersurfaces in ℝ2n . Sci. China Math. 58, 1771–1778 (2015). https://doi.org/10.1007/s11425-014-4903-2
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DOI: https://doi.org/10.1007/s11425-014-4903-2