Bäcklund transformations for the Kirchhoff top.
Bäcklund transformations for the trigonometric Gaudin magnet.
Basics of Lagrangian foliations.
The paper is an exposition of basic known local and global results on Lagrangian foliations such as the Theorem of Darboux-Lie, Weinstein, Arnold-Liouville, a global characterization of cotangent bundles, higher order Maslov classes, etc.
Bidifferential calculus approach to AKNS hierarchies and their solutions.
Bifurcation diagrams and Fomenko’s surgery on Liouville tori of the Kolossoff potential
Bifurcation d'orbites homoclines pour les systèmes hamiltoniens
Bifurcation d'orbites périodiques d'un système hamiltonien au voisinage d'une position d'équilibre
Bifurcation for second-order Hamiltonian systems with periodic boundary conditions.
Bifurcation of periodic and chaotic solutions in discontinuous systems
Chaos generated by the existence of Smale horseshoe is the well-known phenomenon in the theory of dynamical systems. The Poincaré-Andronov-Melnikov periodic and subharmonic bifurcations are also classical results in this theory. The purpose of this note is to extend those results to ordinary differential equations with multivalued perturbations. We present several examples based on our recent achievements in this direction. Singularly perturbed problems are studied as well. Applications are given...
Bifurcations and Hamilton's Principle.
Bifurcations in symplectic space
In this paper we take new steps in the theory of symplectic and isotropic bifurcations, by solving the classification problem under a natural equivalence in several typical cases. Moreover we define the notion of coisotropic varieties and formulate also the coisotropic bifurcation problem. We consider several symplectic invariants of isotropic and coisotropic varieties, providing illustrative examples in the simplest non-trivial cases.
Birational equivalence in the symplectic category.
Birkhoff normal formsand analytic geometry
Birth of an elliptic island in a chaotic sea.
Blow up of mechanical systems with a homogeneous energy.
By using the ideas introduced by McGehee in the study of the singularities in some problems of Celestial Mechanics, we study the singularities at the origin and at the infinity for some classical mechanical systems with homogeneous kinetic and potential energy functions. For these systems the origin and the infinity of the configuration coordinates is usually a singularity or a nullity of the Hamiltonian function and the verctor field. This work generalizes a previous one by the first and the third...
Bohr–Sommerfeld quantization condition for non-selfadjoint operators in dimension 2.
Borel summation and splitting of separatrices for the Hénon map
We study two complex invariant manifolds associated with the parabolic fixed point of the area-preserving Hénon map. A single formal power series corresponds to both of them. The Borel transform of the formal series defines an analytic germ. We explore the Riemann surface and singularities of its analytic continuation. In particular we give a complete description of the “first” singularity and prove that a constant, which describes the splitting of the invariant manifolds, does not vanish. An interpretation...
Bound states in completely integrable systems with two types of particles
Bounded homeomorphisms of the open annulus.
Branching of periodic orbits from Kukles isochrones.