In this paper, we prove that for every index perfect non-degenerate compact star-shaped hypersurface E C R2n, there exist at least n non-hyperbolic closed characteristics with even Maslov- type indices on E when n is ...In this paper, we prove that for every index perfect non-degenerate compact star-shaped hypersurface E C R2n, there exist at least n non-hyperbolic closed characteristics with even Maslov- type indices on E when n is even. When n is odd, there exist at least n closed characteristics with odd Maslov-type indices on E and at least （n - 1） of them are non-hyperbolic. Here we call a compact star-shaped hypersurfaee E ∈R2 index perfect if it carries only finitely many geometrically distinct prime closed characteristics, and every prime closed characteristic （T, y） on E possesses positive mean index and whose Maslov-type index i（y, m） of its m-th iterate satisfies i（y, m） ≠-1 when n is even, and i（y, rn） ≠2{-1,0} when n is odd for all rn E N.展开更多
Let(RP^(n),F)be a bumpy and irreversible Finsler n-dimensional real projective space with reversibilityλand flag curvature K satisfying(λ/1+λ)^(2)<K≤1 when n is odd,and K≥0 when n is even.We show that if there...Let(RP^(n),F)be a bumpy and irreversible Finsler n-dimensional real projective space with reversibilityλand flag curvature K satisfying(λ/1+λ)^(2)<K≤1 when n is odd,and K≥0 when n is even.We show that if there exist exactly 2[n+1/2]prime closed geodesics on such(RP^(n),F),then all of them are non-contractible,which coincides with the Katok’s examples.展开更多
基金supported by NSFC(Grant Nos.11671215,11131004 and 11471169,11401555,11222105 and 11431001)LPMC of MOE of China+3 种基金Anhui Provincial Natural Science Foundation(Grant No.1608085QA01)MCME,LPMC of MOE of ChinaNankai UniversityBAICIT of Capital Normal University
文摘In this paper, we prove that for every index perfect non-degenerate compact star-shaped hypersurface E C R2n, there exist at least n non-hyperbolic closed characteristics with even Maslov- type indices on E when n is even. When n is odd, there exist at least n closed characteristics with odd Maslov-type indices on E and at least （n - 1） of them are non-hyperbolic. Here we call a compact star-shaped hypersurfaee E ∈R2 index perfect if it carries only finitely many geometrically distinct prime closed characteristics, and every prime closed characteristic （T, y） on E possesses positive mean index and whose Maslov-type index i（y, m） of its m-th iterate satisfies i（y, m） ≠-1 when n is even, and i（y, rn） ≠2{-1,0} when n is odd for all rn E N.
基金The first author was partially supported by National Key R&D Program of China(Grant No.2020YFA0713300)NSFC(Grant Nos.11671215 and 11790271)+1 种基金LPMC of MOE of China and Nankai Universitythe second author was partially supported by NSFC(Grant Nos.11771341 and 12022111)。
文摘Let(RP^(n),F)be a bumpy and irreversible Finsler n-dimensional real projective space with reversibilityλand flag curvature K satisfying(λ/1+λ)^(2)<K≤1 when n is odd,and K≥0 when n is even.We show that if there exist exactly 2[n+1/2]prime closed geodesics on such(RP^(n),F),then all of them are non-contractible,which coincides with the Katok’s examples.
