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Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularites, and topological invariants.
The authors, both of whom have contributed significantly to the field, develop the classification theory for integrable systems with two degrees of freedom. This theory allows one to distinguish such systems up to two natural equivalence relations: the equivalence...

Geodesic flows of Riemannian metrics on manifolds are one of the classical objects in geometry. A particular place among them is occupied by integrable geodesic flows. We consider them in the context of the general theory of integrable Hamiltonian systems, and in particular, from the viewpoint of a new topological classification theory, which was recently developed for integrable Hamiltonian systems with two degrees of freedom. As a result, we will see that such a new approach is very useful for a deeper understanding of the topology and geometry of integrable geodesic flows. The main object...

Geodesic flows of Riemannian metrics on manifolds are one of the classical objects in geometry. A particular place among them is occupied by integrable geodesic flows. We consider them in the context of the general theory of integrable Hamiltonian systems, and in particular, from the viewpoint of a new topological classification theory, which was recently developed for integrable Hamiltonian systems with two degrees of freedom. As a result, we will see that such a new approach is very useful for a deeper understanding of the topology and geometry of integrable geodesic flows. The main object...