Deformation quantization
Bifurcations and Hamilton's Principle.
Cohomology of Symplectomorphism Groups and Critical Values of Hamiltonians.
Normal Modes for Nonlinear Hamiltonian Systems.
The Invariance of Poincaré's Generating Function for Canonical Transformations.
Foreword, Contents
Almost invariant submanifolds for compact group actions
We define a distance between submanifolds of a riemannian manifold and show that, if a compact submanifold is not moved too much under the isometric action of a compact group , there is a -invariant submanifold -close to . The proof involves a procedure of averaging nearby submanifolds of riemannian manifolds in a symmetric way. The procedure combines averaging techniques of Cartan, Grove/Karcher, and de la Harpe/Karoubi with Whitney’s idea of realizing submanifolds as zeros of sections...
Extensions of symplectic groupoids and quantization.
Anwendungen der De Rhamschen Zerlegung auf Probleme der lokalen Flächentheorie.
Self-Similarity of Poisson structures on tori
We study the group of diffeomorphisms of a 3-dimensional Poisson torus which preserve the Poisson structure up to a constant multiplier, and the group of similarity ratios.
Quantization and Morita equivalence for constant Dirac structures on tori
We define a -algebraic quantization of constant Dirac structures on tori and prove that -equivalent structures have Morita equivalent quantizations. This completes and extends from the Poisson case a theorem of Rieffel and Schwarz.
Closed Curves on Convex Hypersurfaces and Periods of Nonlinear Oscillations.
Poisson geometry and deformation quantization near a strictly pseudoconvex boundary
Let be a complex manifold with strongly pseudoconvex boundary . If is a defining function for , then is plurisubharmonic on a neighborhood of in , and the (real) 2-form is a symplectic structure on the complement of in a neighborhood of in ; it blows up along . The Poisson structure obtained by inverting extends smoothly across and determines a contact structure on which is the same as the one induced by the complex structure. When is compact, the Poisson structure near...
Page 1