A "Birkhoff-Lewis" type result for a class of Hamiltonian systems.
A Bound for the Fixed-Point Index of an Area-Preserving Map with Applications to Mechanics.
A characterization of isochronous centres in terms of symmetries.
We present a description of isochronous centres of planar vector fields X by means of their groups of symmetries. More precisely, given a normalizer U of X (i.e., [X,U]= µ X, where µ is a scalar function), we provide a necessary and sufficient isochronicity condition based on µ. This criterion extends the result of Sabatini and Villarini that establishes the equivalence between isochronicity and the existence of commutators ([X,U]= 0). We put also special emphasis on the mechanical aspects of isochronicity;...
A characterization of tangent and stable tangent bundles
A construction of realizations of perturbations of Poincaré maps
A convexity theorem for Poisson actions of compact Lie groups
A deterministic displacement theorem for Poisson processes.
A direct proof of a theorem by Kolmogorov in hamiltonian systems
A discretization of the nonholonomic Chaplygin sphere problem.
A dynamical system connected with inhomogeneous 6-vertex model
A field theory for symplectic fibrations over surfaces.
A finite dimensional linear programming approximation of Mather's variational problem
We provide an approximation of Mather variational problem by finite dimensional minimization problems in the framework of Γ-convergence. By a linear programming interpretation as done in [Evans and Gomes, ESAIM: COCV 8 (2002) 693–702] we state a duality theorem for the Mather problem, as well a finite dimensional approximation for the dual problem.
A finite-dimensional integrable system associated with a polynomial eigenvalue problem.
A first-order canonical set of generalized Jacobi-type variables for hyperbolic orbital motion.
A functional analysis approach to Arnold diffusion
A geometric analysis of dynamical systems with singular Lagrangians
We study dynamics of singular Lagrangian systems described by implicit differential equations from a geometric point of view using the exterior differential systems approach. We analyze a concrete Lagrangian previously studied by other authors by methods of Dirac’s constraint theory, and find its complete dynamics.
A geometric approach to a result of Benci and Giannoni for Hamiltonian systems with singular potentials.
A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: announcement of results.
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...