Related papers: The Hyperbolic Heisenberg and Sigma Models in (1+1…
This is the second part of a work aimed to study complex-phase oscillatory solutions of nonlinear symmetric hyperbolic systems. We consider, in particular, the case of one space dimension. That is a remarkable case, since one can always…
In this article we will study the existence and nonexistence of sign changing solutions for the Brezis-Nirenberg type problem in the Hyperbolic space. We will also establish sharp asymptotic estimates for the solutions and the compactness…
The topic of this article is the numerical search of codimension 2 Normally Hyperbolic Invariant Manifolds (NHIM) in Hamiltonian systems with 3 degrees of freedom and their internal dynamics. We point out relations between different…
A N-sized inertial classical Heisenberg ferromagnet, which consists in a modification of the well-known standard model, where the spins are replaced by classical rotators, is studied in the limit of infinite-range interactions. The usual…
In this article, we study geometric aspects of semi-arithmetic Riemann surfaces by means of number theory and hyperbolic geometry. First, we show the existence of infinitely many semi-arithmetic Riemann surfaces of various shapes and prove…
We present a classification of the hyperbolic Kac-Moody (HKM) superalgebras. The HKM superalgebras of rank larger or equal than 3 are finite in number (213) and limited in rank (6). The Dynkin-Kac diagrams and the corresponding simple root…
We study lattice points on hyperbolic circles centred at Heegner points of class number one. Our main result is that, on a density one subset of radii tending to infinity, the angles of such points equidistribute on the unit circle. To…
We revisit the early work of Minkowski and Sommerfeld concerning hyperbolic motion, and we describe some geometrical aspects of the electrodynamic interaction. We discuss the advantages of a time symmetric formulation in which the material…
We use spin-coherent states as a time-dependent variational ansatz for a semiclassical description of a large family of Heisenberg models. In addition to common approaches we also evaluate the square variance of the Hamiltonian in terms of…
A major challenge in the study of the structure of the three-dimensional homology cobordism group is to understand the interaction between hyperbolic geometry and homology cobordism. In this paper, for a hyperbolic homology sphere $Y$ we…
An abstract first order differential equation of hyperbolic type with drift term on a Riemannian manifold is considered. For proving its well-posedness, transmutator and commutator relations are needed, which are studied in a general…
The representations of Clifford algebras and their involutions and anti-involutions are fully investigated since decades. However, these representations do sometimes not comply with usual conventions within physics. A few simple examples…
The aim of this paper is twofold. First, we introduce standard blenders (special hyperbolic sets) and their variations, and prove their fundamental properties on the generation of $C^1$-robust tangencies. In particular, these blenders…
We derive and analyze exact static solutions to the gravitating O(3) $\sigma$ model with cosmological constant in (2+1) dimensions. Both signs of the gravitational and cosmological constants are considered. Our solutions include…
We establish existence and uniqueness results for the singular initial value problem associated with a class of quasilinear, symmetric hyperbolic, partial differential equations of Fuchsian type in several space dimensions. This is an…
Representing data in hyperbolic space can effectively capture latent hierarchical relationships. With the goal of enabling accurate classification of points in hyperbolic space while respecting their hyperbolic geometry, we introduce…
An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…
Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…
We study the superspace formulation of the noncommutative nonlinear supersymmetric O(N) invariant sigma-model in 2+1 dimensions. We prove that the model is renormalizable to all orders of 1/N and explicitly verify that the model is…
We consider random hyperbolic graphs in hyperbolic spaces of any dimension $d+1\geq 2$. We present a rescaling of model parameters that casts the random hyperbolic graph model of any dimension to a unified mathematical framework, leaving…