2014
DOI: 10.1007/s40304-015-0047-0
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Symmetric Closed Characteristics on Symmetric Compact Convex Hypersurfaces in $$\mathbf{R}^8$$ R 8

Abstract: Let be a C 3 compact symmetric convex hypersurface in R 8 . We prove that when carries exactly four geometrically distinct closed characteristics, then all of them must be symmetric. Due to the example of weakly non-resonant ellipsoids, our result is sharp.

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“…invariant under the symmetry). In low dimensional cases, this result is proved in [22,30] for a particular symmetry, but without the nondegeneracy assumption.…”
Section: Introductionmentioning
confidence: 84%
“…invariant under the symmetry). In low dimensional cases, this result is proved in [22,30] for a particular symmetry, but without the nondegeneracy assumption.…”
Section: Introductionmentioning
confidence: 84%
“…for all ∈ SH con (2n) with n = 2 or 3 provided # T ( ) = n. The second result is that (1.2) holds for all ∈ SH con (8) provided # T ( ) = 4 proved by Liu, Long, Wang and Zhang recently in [18]. But in general, whether (1.2) holds for every ∈ SH st (2n) is still open.…”
Section: Introduction and Main Resultsmentioning
confidence: 99%