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- W1845250906 abstract "In this paper, we prove that for every index perfect non-degenerate compact star-shaped hypersurface $Sigmasubset{bf R}^{2n}$, there exist at least $n$ non-hyperbolic closed characteristics with even Maslov-type indices on $Sigma$ when $n$ is even. When $n$ is odd, there exist at least $n$ closed characteristics with odd Maslov-type indices on $Sigma$ and at least $(n-1)$ of them are non-hyperbolic. Here we call a compact star-shaped hypersurface $Sigmasubset {bf R}^{2n}$ {rm index perfect} if it carries only finitely many geometrically distinct prime closed characteristics, and every prime closed characteristic $(tau,y)$ on $Sigma$ possesses positive mean index and whose Maslov-type index $i(y, m)$ of its $m$-th iterate satisfies $i(y, m)not= -1$ when $n$ is even, and $i(y, m)notin {-2,-1,0}$ when $n$ is odd for all $min {bf N}$." @default.
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- W1845250906 date "2015-10-29" @default.
- W1845250906 modified "2023-09-22" @default.
- W1845250906 title "Non-hyperbolic closed characteristics on non-degenerate star-shaped hypersurfaces in ${bf R}^{2n}$" @default.
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