On implicit Lagrangian differential systems
Let (P,ω) be a symplectic manifold. We find an integrability condition for an implicit differential system D' which is formed by a Lagrangian submanifold in the canonical symplectic tangent bundle (TP,ὡ).
Systems of rays in the presence of distribution of hyperplanes
Horizontal systems of rays arise in the study of integral curves of Hamiltonian systems on T*X, which are tangent to a given distribution V of hyperplanes on X. We investigate the local properties of systems of rays for general pairs (H,V) as well as for Hamiltonians H such that the corresponding Hamiltonian vector fields are horizontal with respect to V. As an example we explicitly calculate the space of horizontal geodesics and the corresponding systems of rays for the canonical distribution...
Logarithmic structure of the generalized bifurcation set
Let be a holomorphic family of functions. If , is an analytic variety then is a natural generalization of the bifurcation variety of G. We investigate the local structure of for locally trivial deformations of . In particular, we construct an algorithm for determining logarithmic stratifications provided G is versal.
Coisotropic varieties and their generating families
On Arnold’s singularities of type
The article contains no abstract
Relative generic singularities of the exponential map
On Martinet's singular symplectic structures
Normal forms of symplectic structures on the stratified spaces
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.
Page 1