Displaying similar documents to “Numerical study of invariant sets of a quasiperiodic perturbation of a symplectic map.”

Invariant properties of the generalized canonical mappings

Stanisław Janeczko (1999)

Banach Center Publications

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One of the fundamental objectives of the theory of symplectic singularities is to study the symplectic invariants appearing in various geometrical contexts. In the paper we generalize the symplectic cohomological invariant to the class of generalized canonical mappings. We analyze the global structure of Lagrangian Grassmannian in the product symplectic space and describe the local properties of generic symplectic relations.

Symplectic Capacities in Manifolds

Alfred Künzle (1997)

Banach Center Publications

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Symplectic capacities coinciding on convex sets in the standard symplectic vector space are extended to any subsets of symplectic manifolds. It is shown that, using embeddings of non-smooth convex sets and a product formula, calculations of some capacities become very simple. Moreover, it is proved that there exist such capacities which are distinct and that there are star-shaped domains diffeomorphic to the ball but not symplectomorphic to any convex set.

Symplectic spinor valued forms and invariant operators acting between them

Svatopluk Krýsl (2006)

Archivum Mathematicum

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Exterior differential forms with values in the (Kostant’s) symplectic spinor bundle on a manifold with a given metaplectic structure are decomposed into invariant subspaces. Projections to these invariant subspaces of a covariant derivative associated to a torsion-free symplectic connection are described.