In this study, we investigate Hamiltonian cycles in the right-Cayley graphs of gyrogroups. More specifically, give a gyrogroup version factor group lemma and show that some certain gyrogroups are Hamiltonian.

We describe the reduction procedure for a symplectic Lie algebroid by a Lie subalgebroid and a symmetry Lie group. Moreover, given an invariant Hamiltonian function we obtain the corresponding reduced Hamiltonian dynamics. Several examples illustrate the generality of the theory.

In this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent Hamiltonians. We drive the time-dependent recursion relations for the renormalized tight-binding Hamiltonian by decimating selective sites of lattice iteratively. The formalism is then used for the calculation of the local density of electronic states for a one dimensional quant...

in this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent hamiltonians. we drive the time-dependent recursion relations for the renormalized tight-binding hamiltonian by decimating selective sites of lattice iteratively. the formalism is then used for the calculation of the local density of electronic states for a one dimensional quant...

Hamiltonian cycles on planar random lattices are considered. The generating function for the number of Hamiltonian cycles is obtained and its singularity is studied. Hamiltonian cycles have often been used to model collapsed polymer globules[1]. A Hamiltonian cycle of a graph is a closed path which visits each of the vertices once and only once. The number of Hamiltonian cycles on a lattice cor...

The main result of this paper is Theorem 2.13 which says that the quotient μ({1})/U associated to a quasi-hamiltonian space (M,ω, μ : M → U) has a symplectic structure even when 1 is not a regular value of the momentum map μ. Namely, it is a disjoint union of symplectic manifolds of possibly different dimensions, which generalizes the result of Alekseev, Malkin and Meinrenken in [AMM98]. We ill...

Classical mechanical systems are modeled by a symplectic manifold (M,ω), and their symmetries are encoded in the action of a Lie group G on M by diffeomorphisms which preserve ω. These actions, which are called symplectic, have been studied in the past forty years, following the works of Atiyah, Delzant, Duistermaat, Guillemin, Heckman, Kostant, Souriau, and Sternberg in the 1970s and 1980s on ...

The group Hameo (M, ω) of Hamiltonian homeomorphisms of a connected symplectic manifold (M, ω) was defined and studied in [7] and further in [6]. In these papers, the authors consistently used the L-Hofer norm (and not the L∞-Hofer norm) on the space of Hamiltonian paths (see below for the definitions). A justification for this choice was given in [7]. In this article we study the L∞-case. In v...