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 Lie systems in quantum mechanics and control theory
Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum problems can be treated in a similar way, may be up to the replacement of the Lie group involved by a central extension of it. The geometric techniques developed for dealing with Lie systems are also used in problems of control theory. Specifically, we will study...
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.
Approximative sequences and almost homoclinic solutions for a class of second order perturbed Hamiltonian systems
In this work we will consider a class of second order perturbed Hamiltonian systems of the form , where t ∈ ℝ, q ∈ ℝⁿ, with a superquadratic growth condition on a time periodic potential V: ℝ × ℝⁿ → ℝ and a small aperiodic forcing term f: ℝ → ℝⁿ. To get an almost homoclinic solution we approximate the original system by time periodic ones with larger and larger time periods. These approximative systems admit periodic solutions, and an almost homoclinic solution for the original system is obtained...
Area preserving group actions on surfaces.
Area preserving homeomorphisms of open surfaces of genus zero.
Arithmétique des rapports de similitudes symplectiques
Arnold diffusion: a variational construction.
Asymptotic solutions for large time of Hamilton–Jacobi equations in euclidean n space
Asymptotic stability for perturbed hamiltonian systems, II
Asymptotic stability of dynamical systems with multiplicative perturbations
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