Related papers: Counting Hyperbolic Components
This paper presents a collection of useful formulas of dynamic derivatives on time scales, systematically collected for reference purposes. As an application, we define trigonometric and hyperbolic functions on time scales in such a way the…
The existence of hyperbolic orbits is proved for a class of singular Hamiltonian systems with repulsive potentials by taking limit for a sequence of periodic solutions which are the minimizers of variational functional
Every real hyperbolic form in three variables can be realized as the determinant of a linear net of Hermitian matrices containing a positive definite matrix. Such representations are an algebraic certificate for the hyperbolicity of the…
Hyperbolic polynomials are real polynomials whose real hypersurfaces are nested ovaloids, the inner most of which is convex. These polynomials appear in many areas of mathematics, including optimization, combinatorics and differential…
We calculate the modulus of curve families inside a hyperbolic quadrilateral and a hyperbolic annulus.
Let $G$ be either a non-elementary (word) hyperbolic group or a large group (both in the sense of Gromov). In this paper we describe several approaches for constructing continuous families of periodic quotients of $G$ with various…
We suggest a new approach to the study of relatively hyperbolic groups based on relative isoperimetric inequalities. Various geometric, algebraic, and algorithmic properties are discussed.
By analogy to the theory of harmonic fields on the complex plane, we build the theory of wave-like fields on the plane of double variable. We construct the hyperbolic analogues of point vortices, sources, vortice-sources and their…
For arbitrary second-order differential operators, the existence conditions and the construction of intertwining transmutation operators are shown. In an explicit form found hyperbolic equations with two independent variables and their…
We investigate number systems for the ring of integers of hyperbolic and dual numbers. We characterize all canonical number systems providing radix form for hyperbolic and dual numbers. Our approach allows us to get suitable bases by means…
In this note, we prove combinatorial formulas for $h^{2,1}$ of prime toric divisors in an arbitrary toric hypersurface Calabi-Yau fourfold $Y_4.$ We show that it is possible to find a toric hypersurface Calabi-Yau in which there are more…
This paper studies the combinatorial Yamabe flow on hyperbolic bordered surfaces. We show that the flow exists for all time and converges exponentially fast to conformal factor which produces a hyperbolic surface whose lengths of boundary…
In this paper we establish a closing property and a hyperbolic closing property for thin trapped chain hyperbolic homoclinic classes with one dimensional center in partial hyperbolicity setting. Taking advantage of theses properties, we…
In this paper we investigate the theory of cuspidalisation of sections of arithmetic fundamental groups of hyperbolic curves to cuspidally i-th and 2/p-th step prosolvable arithmetic fundamental groups. As a consequence we exhibit two,…
This article is a first step in the study of equations in periodic groups. As an application, we study the structure of periodic quotients of hyperbolic groups. We investigate for instance the Hopf and co-Hopf properties, the isomorphism…
We call a log variety (X, D) algebraically hyperbolic if there exists a positive number e such that 2g(C) - 2 + i(C, D) >= e deg(C) for all curves C on X, where i(C, D) is the number of the intersections between D and the normalization of…
We consider hyperbolic equations with time-dependent coefficients and develop an abstract framework to derive the asymptotic behaviour of the representation of solutions for large times. We are dealing with generic situations where the…
In this article we review the basics of the phasor formalism in a rigorous way, highlighting the physical motivation behind it and presenting a hyperbolic counterpart of the phasor addition formula.
We give an effective estimate for the totally ramified value number of the hyperbolic Gauss maps of complete flat fronts in the hyperbolic three-space. As a corollary, we give the upper bound of the number of exceptional values of them for…
A classical problem in Complex Dynamics on hyperbolic domains is to characterize the hyperbolic step of parabolic functions. This topic has been studied by several authors, leading to different results and providing characterizations that…