Abstract
The paper concerns the existence of rotating periodic solutions in Hamiltonian systems. This kind of rotating periodic solutions has the form of x(t+T)=Qx(t) with some symplectic orthogonal matrix Q. When Qk=I for some integer k>0, it is a symmetric periodic solution and when Qk≠I for any k∈N+, it is just a quasi-periodic one corresponding to a rotation. It is proved that if the Hamiltonian is strictly convex, coercive and Q invariant, then there exists a Q-rotating periodic solution on every energy surface.
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