Related papers: Hamiltonian vector fields on almost symplectic man…

In this paper we consider the length minimizing properties of Hamiltonian paths generated by quasi-autonomous Hamiltonians on symplectically aspherical manifolds. Motivated by the work of L. Polterovich and M. Schwarz, we study the role of…

A (quasi-)Hamiltonian manifold is called multiplicity free if all of its symplectic reductions are 0-dimensional. In this paper, we classify multiplicity free Hamiltonian actions for (twisted) loop groups or, equivalently, multiplicity free…

Consider a symplectic circle action on a closed symplectic manifold with non-empty isolated fixed points. Associated to each fixed point, there are well-defined non-zero integers, called weights. We prove that the action is Hamiltonian if…

This paper presents a method for learning Hamiltonian dynamics from a limited set of data points. The Hamiltonian vector field is found by regularized optimization over a reproducing kernel Hilbert space of vector fields that are inherently…

We show that the quotient associated to a quasi-Hamiltonian space has a symplectic structure even when 1 is not a regular value of the momentum map: it is a disjoint union of symplectic manifolds of possibly different dimensions, which…

The Hamiltonian formalism is extremely elegant and convenient to mechanics problems. However, its application to the classical field theories is a difficult task. In fact, you can set one to one correspondence between the Lagrangian and…

In the present paper, we characterize almost Kenmotsu manifolds admitting holomorphically planar conformal vector (HPCV) fields. We have shown that if an almost Kenmotsu manifold $M^{2n+1}$ admits a non-zero HPCV field $V$ such that $\phi V…

We establish normal forms for conformal vector fields on pseudo-Riemannian manifolds in the neighborhood of a singularity. For real-analytic Lorentzian manifolds, we show that the vector field is analytically linearizable or the manifold is…

We study, theoretically and experimentally, a 1-parameter family of transformations and their limiting vector field on the space of plane polygons. These transformations are discrete analogs of completely integrable transformation on closed…

Let $M^{2n}$ be a Poisson manifold with Poisson bivector field $\Pi$. We say that $M$ is b-Poisson if the map $\Pi^n:M\to\Lambda^{2n}(TM)$ intersects the zero section transversally on a codimension one submanifold $Z\subset M$. This paper…

Let $M$ be a non-compact connected manifold with a cocompact and properly discontinuous action of a discrete group $G$. We establish a Poincar\'{e}-Hopf theorem for a bounded vector field on $M$ satisfying a mild condition on zeros. As an…

The Hamiltonian Monte Carlo method generates samples by introducing a mechanical system that explores the target density. For distributions on manifolds it is not always simple to perform the mechanics as a result of the lack of global…

Let $\text{Ham(M,L)}$ denote the group of Hamiltonian diffeomorphisms on a symplectic manifold $M$, leaving a Lagrangian submanifold $L\subset M$ invariant. In this paper, we show that $\text{Ham(M,L)}$ has the fragmentation property, using…

We show, by an elementary and explicit construction, that the group of Hamiltonian diffeomorphisms of certain symplectic manifolds, endowed with Hofer's metric, contains subgroups quasi-isometric to Euclidean spaces of arbitrary dimension.

We study multisymplectic structures taking values in vector bundles with connections from the viewpoint of the Hamiltonian symmetry. We introduce the notion of bundle-valued $n$-plectic structures and exhibit some properties of them. In…

The (local) invariant symplectic action functional $\A$ is associated to a Hamiltonian action of a compact connected Lie group $\G$ on a symplectic manifold $(M,\omega)$, endowed with a $\G$-invariant Riemannian metric $<\cdot,\cdot>_M$. It…

The paper reviews the notion of $n+\frac{1}{2}$D non-autonomous Hamiltonian systems, portraying their dynamics as the flow of the Reeb field related to a closed two-form of maximal rank on a cosymplectic manifold, and naturally decomposing…

We show that if (M,\omega) is a closed symplectic manifold which admits a nontrivial Hamiltonian vector field all of whose contractible closed orbits are constant, then Hofer's metric on the group of Hamiltonian diffeomorphisms of…

Let $M$ be a symplectic manifold, equipped with a semifree symplectic circle action with a finite, nonempty fixed point set. We show that the circle action must be Hamiltonian, and $M$ must have the equivariant cohomology and Chern classes…

Using methods from symplectic topology, we prove existence of invariant variational measures associated to the flow $\phi_H$ of a Hamiltonian $H\in C^{\infty}(M)$ on a symplectic manifold $(M,\omega)$. These measures coincide with Mather…