We study the dynamics near transverse intersections of stable and unstable manifolds of sheets of symmetric periodic orbits in reversible systems. We prove that the dynamics near such homoclinic and heteroclinic intersections is not C1 structurally stable. This is in marked contrast to the dynamics

We prove a result about extension of a minimal AF-equivalence relation R on the Cantor set X, the extension being ‘small ’ in the sense that we modify R on a thin closed subset Y of X. We show that the resulting extended equivalence relation S is orbit equivalent to the original R, and so, in particular, S is affable. Even in the simplest case—when Y is a finite set—this result is highly non-trivial. The result itself—called the absorption theorem—is a

Abstract not found

Abstract. We consider fractal percolation (or Mandelbrot percolation) which is one of the most well studied example of random Cantor sets. Rams and the first author [9] studied the projections (orthogonal, radial and co-radial) of fractal percolation sets on the plane. We extend their results to higher dimension. 1.

Abstract. Let M be a smooth compact Riemannian manifold without boundary, and φ:M × IR→M a transitive Anosov flow. We prove that if the time one map of φ is C1-approximated by Axiom A diffeomor-phisms with more than one attractor, then φ is topologically equivalent to the suspension of an Anosov diffeomorphism.

Abstract not found

Abstract For non-reversible Finsler metrics of positive flag curvature on spheres and projective spaces we present results about the number and the length of closed geodesics and about their stability properties.

Abstract. This paper is devoted to a study of the multiple recurrence of two commuting transformations. We derive a result which is similar but not identical to that of one single transformation established by Bergelson, Host and Kra. We will use the machinery of “magic systems ” established

Abstract not found

Abstract not found