Abstract:We consider a planar Hamiltonian system of the type Jz = ∇ z H(t, z), where H : R × R 2 → R is a function periodic in the time variable, such that ∇ z H(t, 0) ≡ 0 and ∇ z H(t, z) is asymptotically linear for |z| → +∞. After revisiting the index theory for linear planar Hamiltonian systems, by using the Poincaré-Birkhoff fixed point theorem we prove that the above nonlinear system has subharmonic solutions of any order k large enough, whenever the rotation numbers (or, equivalently, the mean Conley-Zehnder indi… Show more
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