Related papers: Normalization of the Hamiltonian and the action sp…

This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…

We generalize symplectic convexity theorems for Hamiltonian actions with proper momentum maps to symplectic actions on orbifolds with mod-$\Gamma$ proper momentum maps.

In this paper, we classify Hamiltonian $S^1$-actions on compact, four dimensional symplectic orbifolds that have isolated singular points with cyclic orbifold structure groups, thus extending the classification due to Karshon to the…

We study the orbit structure and the geometric quantization of a pair of mutually commuting hamiltonian actions on a symplectic manifold. If the pair of actions fulfils a symplectic Howe condition, we show that there is a canonical…

We derive a normal form for a near-integrable, four-dimensional symplectic map with a fold or cusp singularity in its frequency mapping. The normal form is obtained for when the frequency is near a resonance and the mapping is approximately…

Let $M$ be a compact orientable surface equipped with a volume form $\omega$, $P$ be either $\mathbb{R}$ or $S^1$, $f:M\to P$ be a $C^{\infty}$ Morse map, and $H$ be the Hamiltonian vector field of $f$ with respect to $\omega$. Let also…

We consider compact connected six dimensional symplectic manifolds with Hamiltonian SU(2) or SO(3) actions with cyclic principal stabilizers. We classify such manifolds up to equivariant symplectomorphisms.

We extend the definition of Weinstein's Action homomorphism to Hamiltonian actions with equivariant moment maps of (possibly infinite-dimensional) Lie groups on symplectic manifolds, and show that under conditions including a uniform bound…

Given a symplectic manifold $(M,\omega)$ endowed with a proper Hamiltonian action of a Lie group $G$, we consider the action induced by a Lie subgroup $H$ of $G$. We propose a construction for two compatible Witt-Artin decompositions of the…

In this paper, we consider Sjamaar's holomorphic slice theorem, the birational equivalence theorem of Guillemin and Sternberg, and a number of important standard constructions that work for Hamiltonian circle actions in both the symplectic…

Hamiltonian quantization of an integral compact symplectic manifold M depends on a choice of compatible almost complex structure J. For open sets U in the set of compatible almost complex structures and small enough values of Planck's…

We propose a new approach to the theory of normal forms for Hamiltonian systems near a non-resonant elliptic singular point. We consider the space of all Hamiltonian functions with such an equilibrium position at the origin and construct a…

In this paper we develop an abstract setup for hamiltonian group actions as follows: Starting with a continuous 2-cochain $\omega$ on a Lie algebra $h$ with values in an $h$-module $V$, we associate subalgebras $sp(h,\omega) \supeq…

This paper examines Hamiltonian actions of non-compact Lie groups on homogeneous bounded domains $X$ in $\mathbb{C}^d$. In the main part, a Lie-theoretical condition for closed subgroups $H$ of the automorphism group of $X$ is described…

Consider a source proper, source connected regular symplectic groupoid acting locally freely and effectively in a Hamiltonian way, and assume that the moment map is proper and has connected fibres. In this case there is an associated…

A simple Hamiltonian manifold is a closed connected symplectic manifold equipped with a Hamiltonian action of a torus T with moment map Phi: M-->t^*, such that the fixed set M^T has exactly two connected components, denoted M_0 and M_1. We…

We study Hamiltonian diffeomorphisms of closed symplectic manifolds with non-contractible periodic orbits. In a variety of settings, we show that the presence of one non-contractible periodic orbit of a Hamiltonian diffeomorphism of a…

We prove that the Seidel morphism of $(M \times M', \omega \oplus \omega')$ is naturally related to the Seidel morphisms of $(M,\omega)$ and $(M',\omega')$, when these manifolds are monotone. We deduce that any homotopy class of loops of…

A closed 3-form $H \in \Omega^3_0(M)$ defines an extension of $\Gamma(TM)$ by $\Omega^2_0(M)$. This fact leads to the definition of the group of $H$-twisted Hamiltonian symmetries $\Ham(M, \JJ; H)$ as well as Hamiltonian action of Lie group…

We prove that on a symplectic sphere, the group of Hamiltonian homeomorphisms in the sense of Oh and M\"uller is a proper normal subgroup of the group of finite energy Hamiltonian homeomorphisms. Moreover we detect infinite-dimensional…