摘要
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.
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
supported by NSFC(Grant Nos.11671215,11131004 and 11471169,11401555,11222105 and 11431001)
LPMC of MOE of China
Anhui Provincial Natural Science Foundation(Grant No.1608085QA01)
MCME,LPMC of MOE of China
Nankai University
BAICIT of Capital Normal University
