Proves that on closed semipositive symplectic manifolds with semisimple quantum homology, Hamiltonian diffeomorphisms exceeding the Betti number in homologically counted contractible fixed points have infinitely many periodic points.
On the Hofer-Zehnder conjecture for non-contractible periodic orbits in Hamiltonian dynamics
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In this paper, we treat an open problem related to the number of periodic orbits of Hamiltonian diffeomorphisms on closed symplectic manifolds. Hofer-Zehnder conjecture states that a Hamiltonian diffeomorphisms has infinitely many periodic orbits if it has "homologically unnecessary periodic orbits"". For example, non-contractible periodic orbits are homologically unnecessary periodic orbits because Floer homology of non-contractible periodic orbits is trivial. We prove Hofer-Zehnder conjecture for non-contractible periodic orbits for very wide classes of symplectic manifolds.
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On the Hofer-Zehnder conjecture for semipositive symplectic manifolds
Proves that on closed semipositive symplectic manifolds with semisimple quantum homology, Hamiltonian diffeomorphisms exceeding the Betti number in homologically counted contractible fixed points have infinitely many periodic points.