Invariant cohomology of the Poisson Lie algebra of a symplectic manifold
Invariant functions on Lie groups and Hamiltonian flows of surface group representations.
Invariant varieties of periodic points for the discrete Euler top.
Invariant vector fields of Hamiltonians
A complete classification of natural transformations of Hamiltonians into vector fields on symplectic manifolds is given herein.
Invariante Variationsprobleme
Invariants homotopiques attachés aux fibrés symplectiques
On donne une construction géométrique d’invariants généralisant la classe de Maslov-Arnold d’une immersion lagrangienne dans un fibré cotangent et l’indice de Maslov-Arnold-Leray d’une immersion lagrangienne -orientée dans : la classe de Maslov-Arnold universelle d’un fibré symplectique et l’indice de Maslov-Arnold-Leray d’un fibré -symplectique, c’est-à-dire dont le groupe structural est le revêtement à feuillets de . Tout ceci relève d’une situation géométrique générale dans laquelle s’introduisent...
Invariants in contact topology.
Invariants of complex structures on nilmanifolds
Let be a simply connected -dimensional nilpotent Lie group endowed with an invariant complex structure. We define a left invariant Riemannian metric on compatible with to be minimal, if it minimizes the norm of the invariant part of the Ricci tensor among all compatible metrics with the same scalar curvature. In [7], J. Lauret proved that minimal metrics (if any) are unique up to isometry and scaling. This uniqueness allows us to distinguish two complex structures with Riemannian data, giving...
Invariants symplectiques et semi-classiques des systèmes intégrables avec singularités
On définit les notions de feuilletages classiques et semi-classiques pour les systèmes complètement intégrables avec singularités. Les résultats de classification standard (telles les coordonnées actions-angles semi-classiques) sont rappelés. Le cas du feuilletage classique de type foyer-foyer est examiné en détail, où des nouveaux invariants semi-globaux apparaissent. Ces invariants sont identifiés dans les conditions de Bohr-Sommerfeld singulières qui donnent le spectre conjoint au voisinage d’une...
Inverse problem of the classical calculus of variations
Involutions of real intervals
This paper shows a simple construction of continuous involutions of real intervals in terms of continuous even functions. We also study smooth involutions defined by symmetric equations. Finally, we review some applications, in particular a characterization of isochronous potentials by means of smooth involutions.
Isometric immersions and the generalized Laplace and elliptic sinh-Gordon equations.
Isometric immersions of space forms and soliton theory.
Isomorphism and Hamilton representation of some nonholonomic systems.
Isomorphisms of Poisson and Jacobi brackets
We present a general theorem describing the isomorphisms of the local Lie algebra structures on the spaces of smooth (real-analytic or holomorphic) functions on smooth (resp. real-analytic, Stein) manifolds, as, for example, those given by Poisson or contact structures. We admit degenerate structures as well, which seems to be new in the literature.
Isospectrality for quantum toric integrable systems
We give a full description of the semiclassical spectral theory of quantum toric integrable systems using microlocal analysis for Toeplitz operators. This allows us to settle affirmatively the isospectral problem for quantum toric integrable systems: the semiclassical joint spectrum of the system, given by a sequence of commuting Toeplitz operators on a sequence of Hilbert spaces, determines the classical integrable system given by the symplectic manifold and commuting Hamiltonians. This type of...
Isotopy of sympletic balls, Gromov' s radius and the structure of ruled symplectic 4-manifolds.
Isotropic characteristic classes