A geometric setting for classical molecular dynamics
A KAM phenomenon for singular holomorphic vector fields
Let X be a germ of holomorphic vector field at the origin of Cn and vanishing there. We assume that X is a good perturbation of a “nondegenerate” singular completely integrable system. The latter is associated to a family of linear diagonal vector fields which is assumed to have nontrivial polynomial first integrals (they are generated by the so called “resonant monomials”). We show that X admits many invariant analytic subsets in a neighborhood of the origin. These are biholomorphic to the intersection...
A KAM-theorem for some nonlinear partial differential equations
A methodology for the numerical computation of normal forms, centre manifolds and first integrals of Hamiltonian systems.
A new degree for -invariant gradient mappings and applications
A new geometrical framework for time-dependent Hamiltonian mechanics.
A new method for measuring the splitting of invariant manifolds
A new obstruction to embedding Lagrangian tori.
A note on a connection between the Poincaré-Arnold-Melnikov integral and the Picard-Vessiot theory
We obtain an algebraic interpretation by means of the Picard-Vessiot theory of a result by Ziglin about the self-intersection of complex separatrices of time-periodically perturbed one-degree of freedom complex analytical Hamiltonian systems.
A note on bidifferential calculi and bihamiltonian systems
In this note we discuss the geometrical relationship between bi-Hamiltonian systems and bi-differential calculi, introduced by Dimakis and Möller–Hoissen.
A note on uniqueness of Cauchy problems associated to planar Hamiltonian systems.
A property of connections of mechanical systems of higher order
A realistic exponential estimate for a paradigm hamiltonian
A recursive scheme of first integrals of the geodesic flow of a Finsler manifold.
A simple proof of the non-integrability of the first and the second Painlevé equations
The first and the second Painlevé equations are explicitly Hamiltonian with time dependent Hamilton function. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems in ℂ⁴. We prove that the latter systems do not have any additional algebraic first integral. In the proof equations in variations with respect to a parameter are used.
A singular lagrangian model for N-body relativistic interactions
A special case of the Garnier system, -polarized abelian surfaces and their moduli
A super-integrable two-dimensional nonlinear oscillator with an exactly solvable quantum analog.
A symplectic fixed point theorem for ...Cpn.
A Symplectic Rigidity Theorem.