New approach to symmetries and singularities in integrable Hamiltonian systems (Q409716)

This article describes new results obtained in the theory of symmetries and singularities of integrable Hamiltonian systems. The paper consists of three parts. In Part 1, a basic overview of the general theory of integrable systems on Lie algebras is provided. The second part is devoted to some new results concerning integrable systems on simple complex Lie algebras in terms of bifurcation diagram and the discriminant of the spectral curve. The last part is devoted to the theory of the symmetrical atoms -- invariants of the two-dimensional integrable systems.