We study the geometry of manifolds carrying symplectic pairs consisting of two closed 2-forms of constant ranks, whose kernel foliations are complementary. Using a variation of the construction of Boothby and Wang we build contact-symplectic and contact pairs from symplectic pairs.

Using odd symplectic structure constructed over tangent bundle of the symplectic manifold, we construct the simple supergeneralization of an arbitrary Hamiltonian mechanics on it. In the case, if the initial mechanics defines Killing vector of some Riemannian metric, corresponding supersymmetric mechanics can be reformulated in the terms of even symplectic structure on the supermanifold. E-MAIL...

In this paper we study symplectic maps with a continuous symmetry group arising by periodic forcing of symmetric Hamiltonian systems. By Noether’s Theorem, for each continuous symmetry the symplectic map has a conserved momentum. We study the persistence of relative periodic points of the symplectic map when momentum is varied and also treat subharmonic persistence and relative subharmonic bifu...

We study the geometry of manifolds carrying symplectic pairs consisting of two closed 2-forms of constant ranks, whose kernel foliations are complementary. Using a variation of the construction of Boothby and Wang we build contact-symplectic and contact pairs from symplectic pairs.

Given a fibration of a symplectic manifold by lagrangian tori, we show that each symplectic vector field splits into two parts : the first is Hamiltonian and the second is symplectic and preserves the fibration. We then show an application of this result in the study of the regular deformations of completely integrable systems.

We discuss the bihamiltonian structure of the Metsaev-Tseytlin superstring in AdS5 ×S 5. We explicitly write down the boost-invariant symplectic structure for the superstring in AdS5 × S 5 and explain its relation to the standard (canonical) symplectic structure. We discuss the geometrical meaning of the boost-invariant symplectic structure for the bosonic string.

1. It is well known that the symplectic algorithms [1][2] for the finite dimensional Hamiltonian systems are very powerful and successful in numerical calculations in comparison with other various non-symplectic computational schemes since the symplectic schemes preserve the symplectic structure in certain sense. On the other hand, the Lagrangian formalism is quie useful for the Hanmiltonian sy...

Symplectic capacities were introduced in 1990 by I. Ekeland and H. Hofer [19, 20] (although the first capacity was in fact constructed by M. Gromov [40]). Since then, lots of new capacities have been defined [16, 30, 32, 44, 49, 59, 60, 90, 99] and they were further studied in [1, 2, 8, 9, 17, 26, 21, 28, 31, 35, 37, 38, 41, 42, 43, 46, 48, 50, 52, 56, 57, 58, 61, 62, 63, 64, 65, 66, 68, 74, 75...

The quaternionic Grassmannian HGr(r, n) is the affine open subscheme of the ordinary Grassmannian parametrizing those 2r-dimensional subspaces of a 2n-dimensional symplectic vector space on which the symplectic form is nondegenerate. In particular there is HP = HGr(1, n+1). For a symplectically oriented cohomology theory A, including oriented theories but also hermitian K-theory, Witt groups an...

We argue that the classical description of a symplectic manifold endowed with a Hamiltonian action of an abelian Lie group G and the corresponding quantum theory can be understood as different aspects of the unitary representation theory of G. To do so, we propose a conceptual analysis of formal tools coming from symplectic geometry (notably, Souriau’s moment map and the Mardsen-Weinstein sympl...