Topic
Symplectic vector space
About: Symplectic vector space is a research topic. Over the lifetime, 2048 publications have been published within this topic receiving 53456 citations.
Papers published on a yearly basis
Papers
More filters
Posted Content•
TL;DR: In this paper, it was shown that any 4-dimensional manifold is essentially made of finitely many symplectic ellipsoids and the key tool is a singular analogue of Donaldson's symplectic hypersurfaces in irrational symplectic manifolds.
Abstract: We prove in this paper that any 4-dimensional symplectic manifold is essentially made of finitely many symplectic ellipsoids The key tool is a singular analogue of Donaldson's symplectic hypersurfaces in irrational symplectic manifolds
9 citations
TL;DR: In this paper, a nonresonance symplectic manifold is considered under the assumption that a smooth symplectic action of a commutative Lie group with compact coisotropic orbits is defined on it.
Abstract: A symplectic manifold is considered under the assumption that a smooth symplectic action of a commutative Lie group with compact coisotropic orbits is defined on it. The problem of existence of variables of the action-angle type is investigated with a view to giving a detailed description of flows in Hamiltonian systems with invariant Hamiltonians. We introduce the notion of a nonresonance symplectic structure for which the problem of recognition of resonance and nonresonance tori is solved.
9 citations
TL;DR: In this paper, the authors constructed two new optimal third-order force-gradient symplectic algorithms in each of which the norm of fourth-order truncation errors is minimized, and they are both not explicitly superior to their no-optimal counterparts in the numerical stability and the topology structure-preserving, but they are in the accuracy of energy on classical problems.
Abstract: With the natural splitting of a Hamiltonian system into kinetic energy and potential energy, we construct two new optimal thirdorder force-gradient symplectic algorithms in each of which the norm of fourth-order truncation errors is minimized. They are both not explicitly superior to their no-optimal counterparts in the numerical stability and the topology structure-preserving, but they are in the accuracy of energy on classical problems and in one of the energy eigenvalues for one-dimensional time-independent Schrodinger equations. In particular, they are much better than the optimal third-order non-gradient symplectic method. They also have an advantage over the fourth-order non-gradient symplectic integrator.
9 citations
13 Jan 2011
TL;DR: In this article, it was shown that a real Bott manifold admits a symplectic form if and only if it is cohomologically symplectic and if it admits even a Kahler structure.
Abstract: A real Bott manifold is the total space of an iterated ℝP 1 -bundle over a point, where each ℝP 1 -bundle is the projectivization of a Whitney sum of two real line bundles. In this paper, we characterize real Bott manifolds which admit a symplectic form. In particular, it turns out that a real Bott manifold admits a symplectic form if and only if it is cohomologically symplectic. In this case, it admits even a Kahler structure. We also prove that any symplectic cohomology class of a real Bott manifold can be represented by a symplectic form. Finally, we study the flux of a symplectic real Bott manifold.
9 citations
TL;DR: In this paper, the Lagrange-symplectic form of a non-degenerate Lagrangian function is shown to have a compatible tangent structure, and the corresponding manifold is said to be locally Lagrange symplectic.
Abstract: The symplectic forms which have a compatible tangent structure locally look like the symplectic form of a nondegenerate Lagrangian function. For this reason, the corresponding manifold is said to be locally Lagrange-symplectic. In the paper, we give some elementary properties of these manifolds, and discuss their symplectic reduction.
9 citations