Minimal tori in S4.
Minkowski Plane, Confocal Conics, and Billiards
Models for quadratic algebras associated with second order superintegrable systems in 2D.
Multi-Hamiltonian structures on Beauville's integrable system and its variant.
Multiple Hamiltonian structures for the Ishii's equation.
Multiplicative integrable models from Poisson-Nijenhuis structures
We discuss the role of Poisson-Nijenhuis (PN) geometry in the definition of multiplicative integrable models on symplectic groupoids. These are integrable models that are compatible with the groupoid structure in such a way that the set of contour levels of the hamiltonians in involution inherits a topological groupoid structure. We show that every maximal rank PN structure defines such a model. We consider the examples defined on compact hermitian symmetric spaces studied by F. Bonechi, J. Qiu...
Neumann system and hyperelliptic functions.
Nilpotent and recursive flows.
Nondegenerate systems and generic properties of the integrable Hamiltonian systems
On classical -matrix for the Kowalevski gyrostat on .
On classical series expansions for quasi-periodic motions.
On implicit Lagrangian differential systems
Let (P,ω) be a symplectic manifold. We find an integrability condition for an implicit differential system D' which is formed by a Lagrangian submanifold in the canonical symplectic tangent bundle (TP,ὡ).
On isomorphism of integrable cases of the Euler equations on the bi-Hamiltonian manifolds and .
On Picard-Fuchs type equations related to integrable Hamiltonian systems.
On singularities of Hamiltonian mappings
The notion of an implicit Hamiltonian system-an isotropic mapping H: M → (TM,ω̇) into the tangent bundle endowed with the symplectic structure defined by canonical morphism between tangent and cotangent bundles of M-is studied. The corank one singularities of such systems are classified. Their transversality conditions in the 1-jet space of isotropic mappings are described and the corresponding symplectically invariant algebras of Hamiltonian generating functions are calculated.
On the Birkhoff normal form of a completely integrable hamiltonian system near a fixed point with resonance
On the existence of equations of evolution.
On the topology of an integrable variant of a nonholonomic Suslov problem
Perturbations of Systems Describing the Motion of a Particle in Central Fields
The present paper deals with the KAM-theory conditions for systems describing the motion of a particle in central field.
Poisson-Nijenhuis structures