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Global Weinstein Type Theorem on Multiple Rotating Periodic Solutions for Hamiltonian Systems

Jiamin XingXue YangYong Li
Dec 2022
摘要
This paper concerns the existence of multiple rotating periodic solutions for$2n$ dimensional convex Hamiltonian systems. For the symplectic orthogonalmatrix $Q$, the rotating periodic solution has the form of $z(t+T)=Qz(t)$,which might be periodic, anti-periodic, subharmonic or quasi-periodic accordingto the structure of $Q$. It is proved that there exist at least $n$geometrically distinct rotating periodic solutions on a given convex energysurface under a pinched condition, so our result corresponds to the well knownEkeland and Lasry's theorem on periodic solutions. It seems that this is thefirst attempt to solve the symmetric quasi-periodic problem on the globalenergy surface. In order to prove the result, we introduce a new index onrotating periodic orbits.
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