Related papers: Periodic orbits in a near Yang-Mills potential
We study the forms of the orbits in a symmetric configuration of a realistic model of the H2O molecule with particular emphasis on the periodic orbits. We use an appropriate Poincar\'e surface of section (PSS) and study the distribution of…
In the framework of the spatial circular Hill three-body problem we illustrate the application of symplectic invariants to analyze the network structure of symmetric periodic orbit families. The extensive collection of families within this…
Using heuristic arguments based on the trace formulas, we analytically calculate the semiclassical two-point correlation form factor for a family of rectangular billiards with a barrier of height irrational with respect to the side of the…
This paper is about the existence of periodic orbits near an equilibrium point of a two-degree-of-freedom Hamiltonian system. The equilibrium is supposed to be a nondegenerate minimum of the Hamiltonian. Every sphere-like component of the…
In this paper we consider an $SU(2)$ Yang-Mills field propagating in the $4+1$ dimensional wormhole spacetime. Assuming the spherically symmetric magnetic ansatz the problem reduces to a one dimensional non linear wave equation. This…
We consider Lie G-valued Yang-Mills fields on the space R x G/H, where G/H is a compact nearly K"ahler six-dimensional homogeneous space, and the manifold R x G/H carries a G_2-structure. After imposing a general G-invariance condition,…
Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with prime periods…
We derive a necessary condition for the existence of marginally stable circular orbits of test particles in stationary axisymmetric spacetimes which possess a refection symmetry with respect to the equatorial plane; photon orbits are also…
We performed high-precision magnetization measurements up to 120~T on three compositions of the newly discovered kagome antiferromagnet YCu$_3$(OD)$_{7-x}$Br$_{2+x}$ (YCOB), revealing a previously unobserved 5/9 fractional magnetization…
A family of periodic orbits is proven to exist in the spatial lunar problem that are continuations of a family of consecutive collision orbits, perpendicular to the primary orbit plane. This family emanates from all but two energy values.…
We consider the Yang-Mills (YM) QFT with group $U(N)$. We take a finite lattice regularization $\Lambda\subset a\mathbb Z^d$, $d = 2,3,4$, with $a\in (0,1]$ and $L$ (even) sites on a side. Each bond has a gauge variable $U\in U(N)$. The…
Equilibrium states of ${\cal N}=4$ supersymmetric Yang-Mills theory can be characterized by the temperature and three chemical potentials, corresponding to the ${\rm U}(1)^3$ subgroup of the $R$-symmetry group. We investigate the phase…
We discover a host of infinite periodic families in the 2-primary stable homotopy groups of spheres. We also confirm the existence of many families predicted by Hopkins--Mahowald. These families appear in nineteen different congruence…
We identify and analyze quasiperiodic and chaotic motion patterns in the time evolution of a classical, non-Abelian Bogomol'nyi-Prasad-Sommerfield (BPS) dyon pair at low energies. This system is amenable to the geodesic approximation which…
In a 2D conservative Hamiltonian system there is a formal integral $\Phi$ besides the energy H. This is not convergent near a stable periodic orbit, but it is convergent near an unstable periodic orbit. We explain this difference and we…
We examine the appearance of the experimentally-observed stripe spin-density-wave magnetic order in five different orbital models of the iron pnictide parent compounds. A restricted mean-field ansatz is used to determine the magnetic phase…
We study bifurcations of area-preserving maps, both orientable (symplectic) and non-orientable, with quadratic homoclinic tangencies. We consider one and two parameter general unfoldings and establish results related to the appearance of…
In this study, equilibrium points and periodic orbits in the potential field of asteroids are investigated. We present the linearized equations of motion relative to the equilibrium points and characteristic equations. We find that the…
We calculate the scalar-gravitational quasi-normal modes of equal angular momenta Myers-Perry black holes in odd dimensions. We find a new bar-mode (non-axisymmetric) classical instability for $D \ge 7$. These black holes were previously…
We consider a delay differential equation that occurs in the study of chronic myelogenous leukemia. After shortly reminding some previous results concerning the stability of equilibrium solutions, we concentrate on the study of stability of…