In this paper we study hyperbolic sets with nonempty interior. We prove the folklore theorem that every transitive hyperbolic set with interior is Anosov. We also show that on a compact surface every locally maximal hyperbolic set with nonempty interior is Anosov. Finally, we give examples of hyperbolic sets with nonempty interior for a non-Anosov diffeomorphism.

We consider a coupled PDE system arising in noise reduction problems. In a two dimensional chamber, the acoustic pressure (unwanted noise) is represented by a hyperbolic wave equation. The floor of the chamber is subject to the action of piezo-ceramic patches (smart materials). The goal is to reduce the acoustic pressure by means of the vibrations of the floor which is modelled by a hyperbolic ...

An attractor Λ for a 3-vector field X is singular-hyperbolic if all its singularities are hyperbolic and it is partially hyperbolic with volume expanding central direction. We prove that C singularhyperbolic attractors, for some α > 0, always have zero volume, thus extending an analogous result for uniformly hyperbolic attractors. The same result holds for a class of higher dimensional singular...

In this paper we analyse a pure jump incomplete market where the risky assets can jump upwards or downwards. In this market we show that, when an investor wants to maximise a HARA utility function of his/her terminal wealth, his/her optimal strategy consists of keeping constant proportions of wealth in the risky assets, thus extending the classical Merton result to this market. Finally, we comp...

Abstra t. We onsider fun tions f : R n ! R n whi h are additively homogeneous and monotone in the produ t ordering on R n (topi al fun tions). We show that if some non-empty sub-eigenspa e of f is bounded in the Hilbert semi-norm then f has an additive eigenve tor and we give a Collatz-Wielandt hara terisation of the orresponding eigenvalue. The boundedness ondition is satis ed if a ertain dire...

Thomas Zaslavsky Binghamton University Binghamton, New York, U.S.A. 13902-6000 September 1991 Revised July 1996 Abstra t We hara terize the edge-signed graphs in whi h every \signi ant" positive losed walk (or ombination of walks) has even length, under seven di erent riteria for signi an e, and also those edge-signed graphs whose double overing graph is bipartite. If the property of even lengt...

We investigate the rigidity of hyperbolic cone metrics on 3-manifolds which are isometric gluing of ideal and hyper-ideal tetrahedra in hyperbolic spaces. These metrics will be called ideal and hyperideal hyperbolic polyhedral metrics. It is shown that a hyper-ideal hyperbolic polyhedral metric is determined up to isometry by its curvature and a decorated ideal hyperbolic polyhedral metric is d...

The Volume Conjecture loosely states that the limit of the n-th colored Jones polynomial of a hyperbolic knot, evaluated at the primitive complex n-th root of unity is a sequence of complex numbers that grows exponentially. Moreover, the exponential growth rate is proportional to the hyperbolic volume of the knot. We provide an efficient formula for the colored Jones function of the simplest hy...

We show that for certain closed hyperbolic manifolds, one can nontrivially deform the real hyperbolic structure when it is considered as a real projective structure. It is also shown that in the presence of a mild smoothness hypothesis, the existence of such real projective deformations is equivalent to the question of whether one can nontrivially deform the canonical representation of the real...

In this paper we define a new invariant of the incomplete hyperbolic structures on a 1-cusped finite volume hyperbolic 3-manifold M , called the ortholength invariant. We show that away from a (possibly empty) subvariety of excluded values this invariant both locally parameterises equivalence classes of hyperbolic structures and is a complete invariant of the Dehn fillings of M which admit a hy...