We present a systematic study of static solutions of the vacuum Einstein equations with negative cosmological constant which asymptotically approach the generalized Kottler ~‘‘Schwarzschild–anti-de Sitter’’! solution, within ~mainly! a conformal framework. We show connectedness of conformal infinity for appropriately regular such spacetimes. We give an explicit expression for the Hamiltonian ma...

Motivated by many observations of anomalies in condensed matter systems, we consider a new fundamental Hamiltonian in which condensed matter and nuclear systems are described initially on the same footing. Since it may be possible that the lattice will respond to the mass change associated with a excited nuclear state, we adopt a relativistic description throughout based on a many-particle Dira...

Let G be a Hamiltonian graph. A factor F of G is called a Hamiltonian factor if F contains a Hamiltonian cycle. In this paper, two sufficient conditions are given, which are two neighborhood conditions for a Hamiltonian graph G to have a Hamiltonian factor. Keywords—graph, neighborhood, factor, Hamiltonian factor.

From a kinematical point of view, the geometrical information of hamiltonian chaos is given by the (un)stable directions, while the dynamical information is given by the Lyapunov exponents. The finite time Lyapunov exponents are of particular importance in physics. The spatial variations of the finite time Lyapunov exponent and its associated (un)stable direction are related. Both of them are f...

The goal of this note is to give an elementary and very short solution to equations of motion for the Kovalevskaya top [1]. For this, we use some results from the original papers by Kovalevskaya [1], Kötter [2] and Weber [3] and also the Lax representation from the note [4]. 1. The Kovalevskaya top [1] is one of the most beautiful examples of integrable systems. This is the top for which the pr...

Let M be a Kähler compact manifold and let G be a connected compact subgroup of its full isometry group which it acts in a Hamiltonian fashion on M and it has a one-dimensional center. In this article we analyze the Kähler reduction M λ and the Kähler cut M λ with respect to the Hamiltonian action of the connected component of the center of G which contains the identity, that we will denote by ...

We present and contrast two distinct ways of including extremal black holes in a Lorentzian Hamiltonian quantization of spherically symmetric EinsteinMaxwell theory. First, we formulate the classical Hamiltonian dynamics with boundary conditions appropriate for extremal black holes only. The Hamiltonian contains no surface term at the internal infinity, for reasons related to the vanishing of t...

We examine the occurrence of Bose-Einstein condensation in both nonrelativistic and relativistic systems with no self-interactions in a general setting. A simple condition for the occurrence of Bose-Einstein condensation can be given if we adopt generalized ζ-functions to define the quantum theory. We show that the crucial feature governing Bose-Einstein condensation is the dimension q associat...

We study a billiard in domain bounded by two confocal ellipses. The Hooke potential is placed at the center of This dynamic system turns out to be Liouville integrable. Therefore, we can make topological analysis studying foliation phase manifold integrals. calculate Fomenko–Zieschang invariants (marked molecules) for isoenergy manifolds every level Hamiltonian, and also give examples other int...

The problem of the charged-particle motion in an axisymmetric magnetic-dipole geometry is used to assess validity Hamiltonian guiding-center theory, which includes higher-order corrections associated with polarization induced by magnetic-field nonuniformity. When a magnetically confined orbit regular (i.e., its magnetic moment adiabatically invariant), approximation, conserves both energy and a...