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In this work we construct for a given smooth, generic Hamiltonian $H :\mathbb{S}^1\times\mathbb{T}^n \longrightarrow \mathbb{R}$ on the torus a chainisomorphism $ \Phi_* : \big(C_*(H),\partial^M_*\big) \longrightarrow\big(C_*(H),\partial^F_*\big)$ between the Morse complex of the Hamiltonianaction $A_H$ on the free loop space of the torus $\Lambda_0(\mathbb{T}^n)$ andthe Floer complex. Though both complexes are generated by the critical pointsof $A_H$, their boundary operators differ. Therefore the construction of $\Phi$is based on counting the moduli spaces of hybrid type solutions which involvesstating a new non-Lagrangian boundary value problem for Cauchy-Riemann typeoperators not yet studied in Floer theory.

Isomorphic chain complexes of Hamiltonian dynamics on tori