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This paper is concerned with both observability and observers for a class of systems described by the two-dimensional hyperbolic PDEs with superlinear boundary conditions which can exhibit chaos. The ...
We prove the regularity of solutions to the strain tensor equation on degenerated hyperbolic surfaces $S$ where the Gauss curvature is zero on a part of the boundary. Furthermore, we obtain the densit...
This course was given at ENSET Oran, November 4-9, 2006. It is an introduction to isometric actions of Lie groups on Lorentz manifolds. Several examples are presented, followed by general defi...
We prove results toward classifying compact Lorentz manifolds on which Heisenberg groups act isometrically. We give a general construction, leading to a new example, of codimension-one actions—those...
We prove a structure theorem for compact aspherical Lorentz manifolds with abundant local symmetry. If M is a compact, aspherical, real-analytic, complete Lorentz manifold such that the isometry grou...
In this paper we consider questions of the following type. Let k be a base eld and K=k be a eld extension. Given a geometric object X over a eld K (e.g. a smooth curve of genus g) what is the le...
We establish stable ergodicity of diffeomorphisms with partially hyperbolic attractors whose Lyapunov exponents along the central direction are all negative with respect to invariant SRBmeasur...
Mathematical theory of billiards is a fascinating subject providing a fertile source of new problems as well as conjecture testing in dynamics, geometry, mathematical physics and spectral theory. Th...
One of the major discoveries of the 20th century mathematics is the possibility of random behavior of deterministic systems. There is a hierarchy of chaotic properties for a dynamical systems but on...
We study compact group extensions of hyperbolic diffeomorphisms. We relate mixing properties of such extensions with accessibility properties of their stable and unstable laminations. We show that g...
We show that a smooth compact Riemannian manifold of dimension  2 admits a Bernoulli di eomorphism with nonzero Lyapunov exponents.
We consider a large class of partially hyperbolic systems containing, among others, ane maps, frame ows on negatively curved manifolds and mostly contracting di eomorphisms. If the rate of mixing ...
Consider a one parameter family of diffeomorphisms fε such that f0 is an Anosov element in a standard abelian Anosov action having sufficiently strong mixing properties. Let νε be any u-...
Recently several new phenomena in dynamics were discovered by looking at small perturbations of compact group extensions of hypebolic systems [8, 14]. In view of this it is desirable to develop a gen...
Let €0  O.2; 1/ be a Schottky group, and let † D H 2=€0 be the corresponding hyperbolic surface. Let C.†/ denote the space of unit length geodesic currents on †. The cohom...

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