A singular hyperbolic attractor for flows is a partially hyperbolic at-tractor with singularities (hyperbolic ones) and volume expanding central direction [MPP1]. The geometric Lorenz attractor [GW] is an example of a singular hyperbolic attractor. In this paper we study the perturbations of singular hyperbolic attractors for three-dimensional flows. It is proved that any attractor obtained fro...

Hyperbolic polynomials have their origins in partial diierential equations. We show in this paper that they have applications in interior point methods for convex programming. Each homogeneous hyperbolic polynomial p has an associated open and convex cone called its hyperbolicity cone. We give an explicit representation of this cone in terms of polynomial inequalities. The function F (x) = ? lo...

We show that for any non–elementary hyperbolic group H and any finitely presented group Q, there exists a short exact sequence 1 → N → G → Q → 1, where G is a hyperbolic group and N is a quotient group of H . As an application we construct a hyperbolic group that has the same n–dimensional complex representations as a given finitely generated group, show that adding relations of the form xn = 1...

This paper is the first in a series whose goal is to understand the structure of low-volume complete orientable hyperbolic 3-manifolds. Here we introduce Mom technology and enumerate the hyperbolic Mom-n manifolds for n ≤ 4. Our longterm goal is to show that all low-volume closed and cusped hyperbolic 3-manifolds are obtained by filling a hyperbolic Mom-n manifold, n ≤ 4 and to enumerate the lo...

This paper is devoted to superlensing using hyperbolic metamaterials: the possibility to image an arbitrary object using hyperbolic metamaterials without imposing any conditions on size of the object and the wave length. To this end, two types of schemes are suggested and their analysis are given. The superlensing devices proposed are independent of the object. It is worth noting that the study...

For any hyperbolic complex X and a ∈ X we construct a visual metric ď = ďa on ∂X that makes the Isom(X)-action on ∂X bi-Lipschitz, Möbius, symmetric and conformal. We define a stereographic projection of ďa and show that it is a metric conformally equivalent to ďa. We also introduce a notion of hyperbolic dimension for hyperbolic spaces with group actions. Problems related to hyperbolic dimensi...

We review the near-field radiative heat flux between hyperbolic materials focusing on multilayer hyperbolic meta-materials. We discuss the formation of the hyperbolic bands, the impact of ordering of the multilayer slabs, as well as the impact of the first single layer on the heat transfer. Furthermore, we compare the contribution of surface modes to that of hyperbolic modes. Finally, we also c...

We consider a few applications of Mañé’s C2 Connecting Lemma. These are the C2 creation of homoclinic points associated to a basic set (i.e., isolated transitive hyperbolic set), a C2 locally generic criterion to know whether a given point belongs to the stable set of hyperbolic homoclinic classes, and that measurably hyperbolic diffeomorphisms (i.e., having the closure of supports of all invar...

Hyperbolic cross approximations by some classical orthogonal polynomials/functions in both bounded and unbounded domains are considered in this paper. Optimal error estimates in proper anisotropic weighted Korobov spaces for both regular hyperbolic cross approximations and optimized hyperbolic cross approximations are established. These fundamental approximation results indicate that spectral m...

For every hyperbolic group and more general hyperbolic graphs, we construct an equivariant ideal bicombing: this is a homological analogue of the geodesic flow on negatively curved manifolds. We then construct a cohomological invariant which implies that several Measure Equivalence and Orbit Equivalence rigidity results established in [MSb] hold for all non-elementary hyperbolic groups and thei...