This paper aims at studying a new integrable Hamiltonian system due to valent. This is a Hamiltonian system with two degrees of freedom where the additional integral is polynomial of degree 3. The critical points and the bifurcation diagram of the Hamiltonian are obtained and the non-degeneracy conditions are verified. Thereafter the topology of iso-energy surfaces is found. Also for zero value of one of the parameters, the type of non-degenerate critical points of rank zero is calculated, the bifurcation diagram of the momentum map is constructed and finally the molecules (fomenko invariants) are found.
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