Related papers: Symplectic A-directed Immersions
We show that the asymptotic iteration method converges and yields accurate energies for a perturbed Coulomb model. We also discuss alternative perturbation approaches to that model.
These memos include the research on $\mathcal{G}_{\mathbb{S}}^{alg}$-scheme theory, the definition of symplectic motives over $\mathcal{G}_{\mathbb{S}}^{alg}$-schemes and symplectic motivic cohomology. This presents a new research…
This note describes a correct way to perform the inflation procedures claimed in the papers on embedding ellipsoids, Journ. Top. 2 (2009), 1-22 and 589-623. The idea is to inflate along a collection of transversally and positively…
We show Lie algebra versions of some results on homological finiteness properties of subdirect products of groups, including a version of the 1-2-3 Theorem.
Relations between the symplectically harmonic cohomology and the coeffective cohomology of a symplectic manifold are obtained. This is achieved through a generalization of the latter, which in addition allows us to provide a coeffective…
We propose a reduction procedure for symplectic connections with symmetry. This is applied to coadjoint orbits whose isotropy is reductive.
We show the irreducibility of some unitary representations of the group of symplectomorphisms and the group of contactomorphisms.
The aim of this paper is to obtain an asymptotic expansion for ergodic integrals of translation flows on flat surfaces of higher genus (Theorem 1) and to give a limit theorem for these flows (Theorem 2).
We prove estimates for weak solutions to a class of Dirichlet problems associated to anisotropic elliptic equations with a zero order term.
We describe the structure of the Lie groups endowed with a left-invariant symplectic form, called symplectic Lie groups, in terms of semi-direct products of Lie groups, symplectic reduction and principal bundles with affine fiber. This…
In this work we study some symplectic submanifolds in the cotangent bundle of a factorizable Lie group defined by second class constraints. By applying the Dirac method, we study many issues of these spaces as fundamental Dirac brackets,…
We define virtual immersions, as a generalization of isometric immersions in a pseudo-Riemannian vector space. We show that virtual immersions possess a second fundamental form, which is in general not symmetric. We prove that a manifold…
This contains a list of (mostly very minor) corrections to the book Introduction to Symplectic Topology, Clarendon Press, Oxford, (1995), together with rewritten versions of two lemmas and some additional comments.
We formulate and prove a chain level descent property of symplectic cohomology for involutive covers by compact subsets that take into account the natural algebraic structures that are present. The notion of an involutive cover is reviewed.…
Using the results of \cite{P1}, we get some estimates of warping functions for isometric immersions by changing the target manifolds by some types of Riemannian manifolds: constant space forms and Hermitian symmetric spaces. And we deal…
We construct a fundamental theory of the derived category of non-finite bi-filtered complexes.
Symplectic integration algorithms are well-suited for long-term integrations of Hamiltonian systems because they preserve the geometric structure of the Hamiltonian flow. However, this desirable property is generally lost when adaptive…
In this paper, we investigate the asymptotic error distributions of symplectic methods for stochastic Hamiltonian systems and further provide Hamiltonian-specific analysis that clarifies the superiority of symplectic methods. Our…
We extend the asymptotic Samuel function of an ideal to a filtration and show that many of the good properties of this function for an ideal are true for filtrations. There are, however, interesting differences, which we explore. We study…
This paper studies isometric immersions of space forms by means of a hierarchy of finite dimensional integrable systems in Lax form on loop algebras.