Any geometrically finite polynomial f of degree d ≥ 2 with connected Julia set is accessible by structurally stable sub-hyperbolic polynomials of the same degree. Moreover, they are topologically conjugate to f on their Julia sets.
Let Y be a Riemann surface with compact boundary embedded into a hyperbolic Riemann surface of finite type X. It is proved that the space of deformations D of Y into X is an open subset of the Teichmüller space T(X) of X. Furthermore, D has compact closure if and only if Y is simply connected or isomorphic to a punctured disk, and D= T(X) if and only if the components of X Y are all disks or punctured disks.
Nous étudions les flots d’Anosov sur les variétés compactes de dimension 3 pour lesquels les distributions stable et instable faibles sont de classe . Nous classons tous ces flots lorsqu’ils préservent le volume puis nous construisons une famille d’exemples qui ne préservent pas le volume. Nous classons aussi ces flots sous une hypothèse de “pincement”. En application, nous décrivons les déformations des groupes fuchsiens dans le groupe des difféomorphismes du cercle.
We prove that if A is a basin of immediate attraction to a periodic attracting or parabolic point for a rational map f on the Riemann sphere, then the periodic points in the boundary of A are dense in this boundary. To prove this in the non-simply connected or parabolic situations we prove a more abstract, geometric coding trees version.
2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.In this paper we consider an L^2 type space of scalar functions L^2 M, A (R u iR) which can be, in particular, the usual L^2 space of scalar functions on R u iR. We find conditions for density of polynomials in this space using a connection with the L^2 space of square-integrable matrix-valued functions on R with respect to a non-negative Hermitian matrix measure. The completness of L^2 M, A (R u iR ) is also established.