If G is a word hyperbolic group of cohomological dimension 2, then every subgroup of G of type FP2 is also word hyperbolic. Isoperimetric inequalities are denned for groups of type FP2 and it is shown that the linear isoperimetric inequality in this generalized context is equivalent to word hyperbolicity. A sufficient condition for hyperbolicity of a general graph is given along with an applica...

We prove several new versions of the Hadamard–Perron Theorem, which relates infinitesimal dynamics to local dynamics for a sequence of local diffeomorphisms, and in particular establishes the existence of local stable and unstable manifolds. Our results imply the classical Hadamard–Perron Theorem in both its uniform and non-uniform versions, but also apply much more generally. We introduce a no...

We propose the metric notion of strong hyperbolicity as a way of obtaining hyperbolicity with sharp additional properties. Specifically, strongly hyperbolic spaces are Gromov hyperbolic spaces that are metrically well-behaved at infinity, and, under weak geodesic assumptions, they are strongly bolic as well. We show that CAT(−1) spaces are strongly hyperbolic. On the way, we determine the best ...

We use drifted Brownian motion in warped product model spaces as comparison constructions to show p-hyperbolicity of a large class of submanifolds for p ≥ 2. The condition for p-hyperbolicity is expressed in terms of upper support functions for the radial sectional curvatures of the ambient space and for the radial convexity of the sub-manifold. In the process of showing p-hyperbolicity we also...

Invariant manifolds like tori, spheres and cylinders play an important part in dynamical systems. In engineering, tori correspond with the important phenomenon of multi-frequency oscillations. Normal hyperbolicity guarantees the robustness of these manifolds but in many applications weaker forms of hyperbolicity present more realistic cases and interesting phenomena. We will review the theory a...

This paper continues our investigation of the dynamics of polynomial diffeomorphisms of C 2 carried out in [BS1-7]. There are several reasons why the polynomial diffeomorphisms of C 2 form an interesting family of dynamical systems. Not the least of these is the fact that there are connections with two other areas of dynamics: polynomial maps of C and diffeo-morphisms of R 2 , which have each r...

We investigate the hyperbolicity of the 5, 8, 10, 13 and 16moment Grad systems for two species of particles under the quasineutrality hypothesis. The analysis is based on an asymptotic expansion with respect to the mass ratio. We show that the hyperbolicity of the systems which involve the heat flux as an independent variable requires a limitation on this heat flux.

Defining the notions of Schottky, Landau and Picard properties on a plane domain, the first author [3] proved that a domain in C having any of these properties is equivalent to the hyperbolicity of the domain. In this paper the authors extend these notions to higher-dimensional case and obtain other various equivalent conditions for the hyperbolicity of a complex manifold.