On the local connectivity of limit sets of Kleinian groups
نویسندگان
چکیده
AMS no. 30F40 The main result here is the fact that the limit set of a geometrically finite Kleinian group with connected limit set is locally connected. For an analytically finite Kleinian group with connected limit set, we give necessary and sufficient conditions for the limit set to be locally connected.
منابع مشابه
Topology of Kleinian Groups in Several Dimensions
1. Introduction The goal of this survey is to give an overview (from a topologist's prospective) of the theory of Kleinian groups in higher dimensions. The survey grew out of a series of lectures which I have given in the University of Maryland in Fall of 1991 and which I have decided to update and publish now, in the proceedings of the 3-rd Ahlfors-Bers Colloquium. This survey was greatly innu...
متن کاملAnalyticity of Hausdorff dimension of limit sets of Kleinian groups
We show that the Hausdorff dimension of the limit set is a real analytic function on the deformation space of a certain class of convex co-compact Kleinian groups, which includes all convex co-compact function groups. This extends a result of Ruelle [21] for quasifuchsian groups.
متن کاملWeak Singularity Spectra of the Patterson Measure for Geometrically Finite Kleinian Groups with Parabolic Elements
In this note we determine the weak singularity spectra of the Patterson measure for geometrically nite Kleinian groups with parabolic elements. This`weak multifractal analysis' is based on a further investigation of the Hausdorr dimension of the Jarn k limit sets, which represent the natural generalisation of the sets of well-approximable irrational numbers to the theory of Kleinian groups.
متن کاملSome Rational Maps Whose Julia Sets Are Not Locally Connected
We describe examples of rational maps which are not topologically conjugate to a polynomial and whose Julia sets are connected but not locally connected. Introduction and motivations The dynamics of a rational map f acting on Ĉ is concentrated on its Julia set which is (by definition) the minimal compact set invariant by f and f−1 containing at least three points. The question of local connecti...
متن کاملConstructing Restricted Patterson Measures for Geometrically Infinite Kleinian Groups
In this paper, we study exhaustions, referred to as ρ-restrictions, of arbitrary nonelementary Kleinian groups with at most finitely many bounded parabolic elements. Special emphasis is put on the geometrically infinite case, where we obtain that the limit set of each of these Kleinian groups contains an infinite family of closed subsets, referred to as ρ-restricted limit sets, such that there ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1995