A-cohomologie et opérateurs de récursion
Action-angle coordinates at singularities for analytic integrable systems.
Addendum to: A Bound for the Fixed-Point Index of an Area-Preserving Map with Applications to Mechanics.
Addendum to "On the Variation in the Cohomology of the Symplectic Form of the Reduced Phase Space."
Affine Gelfand-Dickey Brackets and Holomorphic Vector Bundles.
Affinor structures in the oscillation theory
In this paper we consider the system of Hamiltonian differential equations, which determines small oscillations of a dynamical system with n parameters. We demonstrate that this system determines an affinor structure J on the phase space TRⁿ. If J² = ωI, where ω = ±1,0, the phase space can be considered as the biplanar space of elliptic, hyperbolic or parabolic type. In the Euclidean case (Rⁿ = Eⁿ) we obtain the Hopf bundle and its analogs. The bases of these bundles are, respectively, the projective...
Algebras of integrals
Algèbres de Lie, systèmes hamiltoniens, courbes algébriques
Almost contact structures and time-dependent Lagrangians
An Index Theory and Existence of Multiple Brake Orbits for Star-Shaped Hamiltonian Systems
Anosov flows and non-Stein symplectic manifolds
We simplify and generalize McDuff’s construction of symplectic 4-manifolds with disconnected boundary of contact type in terms of the linking pairing defined on the dual of 3-dimensional Lie algebras. This leads us to an observation that an Anosov flow gives rise to a bi-contact structure, i.e. a transverse pair of contact structures with different orientations, and the construction turns out to work for 3-manifolds which admit Anosov flows with smooth invariant volume. Finally, new examples of...
Another approach to the classical calculus of variations. I
Another approach to the classical calculus of variations. III
Another approach to the classical calculus of variations. II. Hamiltonian theory
Appendix (to D. McDuff and L. Polterovich)
Applications of convex integration to symplectic and contact geometry
We apply Gromov’s method of convex integration to problems related to the existence and uniqueness of symplectic and contact structures
Applications of symplectic homology I.
Applications of symplectic homology II: Stability of the action spectrum.
Approximation of invariant surfaces by periodic orbits in high-dimensional maps: Some rigorous results.
Area preserving homeomorphisms of open surfaces of genus zero.