Given a convex n-gon, we can draw n disks (called side disks) where each disk has different of the polygon as diameter and midpoint its center. The intersection graph such is undirected with vertices two are adjacent if only they have point in common. Such was introduced by Huemer Pérez-Lantero (Discrete Mathematics, 2020), proved to be planar Hamiltonian. In this paper, study further combinato...

We introduce the notion of a real form of a Hamiltonian dynamical system in analogy with the notion of real forms for simple Lie algebras. This is done by restricting the complexified initial dynamical system to the fixed point set of a given involution. The resulting subspace is isomorphic (but not symplectomorphic) to the initial phase space. Thus to each real Hamiltonian system we are able t...

A Hamiltonian cycle is a spanning cycle in a graph, i.e., a cycle through every vertex, and a Hamiltonian path is a spanning path. In this paper we present two theorems stating sufficient conditions for a graph to possess Hamiltonian cycles and Hamiltonian paths. The significance of the theorems is discussed, and it is shown that the famous Ore’s theorem directly follows from our result.  2004...

A necessary and sufficient condition is given for quasi-homogeneous polynomial Hamiltonian systems having a center. Then it shown that there exists bound on the number of limit cycles bifurcating from period annulus at any order Melnikov functions; explicit expression this in terms (n,k,s1,s2), where n degree perturbation polynomials, k first nonzero higher function, (s1,s2) weight exponent wit...

We consider a particle governed by one-dimensional Hamiltonian in which artificial periodic spin-orbit coupling and Zeeman lattice have incommensurate periods. Using best rational approximations to such quasiperiodic Hamiltonian, the problem is reduced description of spinor states superlattice. In absence constant splitting, system acquires an additional symmetry, hinders localization. However,...

This work is a continuation of our recent study non-relativistic charged particles, confined to sphere enclosing magnetic dipole at its center. In this sequel, we extend computations in two significant ways. The first relativistic spin-$\frac{1}{2}$ fermion and the second concerns interpretation physics. Whereas previous paper, speculated on possibility observing such condensed matter systems a...

a noninteracting quantum-dot arrays side coupled to a quantum wire is studied. transport through the quantum wire is investigated by using a noninteracting anderson tunneling hamiltonian. the conductance at zero temperature develops an oscillating band with resonances and antiresonances due to constructive and destructive interference in the ballistic channel, respectively. moreover, we have fo...

We present a constructive existence proof that every real skew-Hamiltonian matrix W has a real Hamiltonian square root. The key step in this construction shows how one may bring any such W into a real quasi-Jordan canonical form via symplectic similarity. We show further that every W has infinitely many real Hamiltonian square roots, and give a lower bound on the dimension of the set of all suc...

Abstract In this paper we consider real or complex skew-Hamiltonian/Hamiltonian pencils λS −H, i.e., pencils where S is a skew-Hamiltonian and H is a Hamiltonian matrix. These pencils occur for example in the theory of continuous time, linear quadratic optimal control problems. We reduce these pencils to canonical and Schur-type forms under structure-preserving transformations, i.e., J-congruen...