We introduce quasi-symplectic groupoids and explain their relation with momentum map theories. This approach enables us to unify into a single framework various momentum map theories, including ordinary Hamiltonian G-spaces, Lu’s momentum maps of Poisson group actions, and the group-valued momentum maps of Alekseev–Malkin–Meinrenken. More precisely, we carry out the following program: (1) We de...

It is a fairly longstanding conjecture that if G is any finite group with IG/ > 2 and if X is any set of generators of G then the Cayley graph T(G : X) should have a Hamiltonian cycle. We present experimental results found by computer calculation that support the conjecture. It turns out that in the case where G is a finite quotient of the modular group the Hamiltonian cycles possess remarkable...

In this thesis, we consider smooth optimal control systems that evolve on Lie groups. Pontryagin’s maximum principle allows us to search for local solutions of the optimal control problem by studying an associated Hamiltonian dynamical system. When the associated Hamiltonian function possess symmetries, we can often study the Hamiltonian system in a vector space whose dimension is lower than th...

The unit sphere S can be identified with the unitary group SU(2). Under this identification the unit sphere can be considered as a non-commutative Lie group. The commutation relations for the vector fields of the corresponding Lie algebra define a 2-step sub-Riemannian manifold. We study sub-Riemannian geodesics on this sub-Riemannian manifold making use of the Hamiltonian formalism and solving...

We note an error in [2]. This Erratum will not be published. The paper defines Ham(M,ω) to be the group of Hamiltonian automorphisms, equipped with the C∞-topology, and G as “the group of smooth based loops in Ham(M,ω)”. This is a misleading formulation, since what the paper really means is that elements of G are Hamiltonian loops. If one understands it in that way, then the proof of [2, Lemma ...

The alternating group graph AGn is an interconnection network topology based on the Cayley graph of the alternating group. There are some interesting results concerning the hamiltonicity and the fault tolerant hamiltonicity of the alternating group graphs. In this article, we propose a new concept called panpositionable hamiltonicity. A hamiltonian graph G is panpositionable if for any two diff...

In this paper we study Multiple periodic solutions for a class of non-autonomous and convex Hamiltonian systems and we investigate use some properties of Ekeland index.  

Schwarz showed that when a closed symplectic manifold (M,ω) is symplectically aspherical (i.e. the symplectic form and the first Chern class vanish on π2(M)) then the spectral invariants, which are initially defined on the universal cover of the Hamiltonian group, descend to the Hamiltonian group Ham(M,ω). In this note we describe less stringent conditions on the Chern class and quantum homolog...