Related papers: On Valiron's Theorem

In this paper we investigate some generic properties of a billiard system on a convex table. We show that generically, every hyperbolic periodic point admits some homoclinic orbit.

In this article, we study the gauge theoretic aspects of real and quaternionic parabolic bundles over a real curve $(X, \sigma_X)$, where X is a compact Riemann surface and {\sigma}X is an anti-holomorphic involution. For a fixed real or…

We prove exponential convergence to time-periodic states of the solutions of time-periodic Hamilton-Jacobi equations on the torus, assuming that the Aubry set is the union of a finite number of hyperbolic periodic orbits of the the Euler…

By means of the contour integration method, we evaluate, in closed form, a class of definite integrals involving hyperbolic tangent function.

We prove a criterion for Benjamini-Schramm convergence of periodic orbits of Lie groups. This general observation is then applied to homogeneous spaces and the space of translation surfaces.

The theory of symmetric-hyperbolic systems is useful for constructing smooth solutions of nonlinear wave equations, and for studying their singularities, including shock waves. We present the main techniques which are required to apply the…

This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties…

A set of travelling wave solutions to a hyperbolic generalization of the convection-reaction-diffusion is studied by the methods of local nonlinear alnalysis and numerical simulation. Special attention is paid to displaying appearance of…

The complete lists of vector hyperbolic equations on the sphere that have integrable third order vector isotropic and anisotropic symmetries are presented. Several new integrable hyperbolic vector models are found. By their integrability we…

We prove an inequality which quantifies the idea that a holomorphic self-map of the disc that perturbs two points is close to the identity function.

We observe that fullerene graphs are one-skeletons of polyhedra, which can be realized with all dihedral angles equal to $\pi/2$ in a hyperbolic 3-dimensional space. One of the most important invariants of such a polyhedron is its volume.…

We show some generic (robust) properties of smooth surfaces immersed in the real 3-space (Euclidean, affine or projective), in the neighbourhood of a {\em godron} (term due to R.Thom): an isolated parabolic point at which the (unique)…

The Hessian Topology is a subject with interesting relations with some classical problems of analysis and geometry. In this article we prove a conjecture on this subject stated by V.I. Arnold concerning the number of connected components of…

The following are notes on the geometry of the bidisk. In particular, we examine the properties of equidistant surfaces in the bidisk.

We study hyperbolic polyhedral surfaces with faces isometric to regular hyperbolic polygons satisfying that the total angles at vertices are at least $2\pi.$ The combinatorial information of these surfaces is shown to be identified with…

This paper is an introduction to the hyperbolic geometry of noncommutative polyballs B_n of bounded linear operators on Hilbert spaces. We use the theory of free pluriharmonic functions on polyballs and noncommutative Poisson kernels on…

In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.

Special relativity corresponds to hyperbolic geometry at constant velocity while the so-called general relativity corresponds to hyperbolic geometry of uniformly accelerated systems. Generalized expressions for angular momentum, centrifugal…

We discuss possible generalizations of Vitali convergence theorem when the source and the target are Banach analytic manifolds. These results are then applied to study behavior of holomorphic mappings between Banach analytic manifolds.…

We develop Nevanlinna's theory for a class of holomorphic maps when the source is a disc. Such maps appear in the theory of foliations by Riemann Surfaces.