A note on the structure of quadratic Julia sets
نویسنده
چکیده
In a series of papers, Bandt and the author have given a symbolic and topological description of locally connected quadratic Julia sets by use of special closed equivalence relations on the circle called Julia equivalences. These equivalence relations reflect the landing behaviour of external rays in the case of local connectivity, and do not apply completely if a Julia set is connected but fails to be locally connected. However, rational external rays land also in the general case. The present note shows that for a quadratic map which does not possess an irrational indifferent periodic orbit and has a connected Julia set the following holds: The equivalence relation induced by the landing behaviour of rational external rays forms the rational part of a Julia
منابع مشابه
Notes on Tan ’ s theorem on similarity between the Mandelbrot set and the Julia sets ∗
This note gives a simplified proof of the similarity between the Mandelbrot set and the quadratic Julia sets at the Misiurewicz parameters, originally due to Tan Lei [TL]. We also give an alternative proof of the global linearization theorem of repelling fixed points. 1 Simlarity between M and J We first give a proof of Tan’s theorem, in a way inspired by Schwick [Sch]. The Julia sets and the M...
متن کاملA Note on Belief Structures and S-approximation Spaces
We study relations between evidence theory and S-approximation spaces. Both theories have their roots in the analysis of Dempsterchr('39')s multivalued mappings and lower and upper probabilities, and have close relations to rough sets. We show that an S-approximation space, satisfying a monotonicity condition, can induce a natural belief structure which is a fundamental block in evidence theory...
متن کاملA Note on Quadratic Maps for Hilbert Space Operators
In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...
متن کاملAnalytical aspects of the interval unilateral quadratic matrix equations and their united solution sets
This paper introduces the emph{interval unilateral quadratic matrix equation}, $IUQe$ and attempts to find various analytical results on its AE-solution sets in which $A,B$ and $CCC$ are known real interval matrices, while $X$ is an unknown matrix. These results are derived from a generalization of some results of Shary. We also give sufficient conditions for non-emptiness of some quasi-solutio...
متن کاملThe Solar Julia Sets of Basic Quadratic Cremer Polynomials
In general, little is known about the exact topological structure of Julia sets containing a Cremer point. In this paper we show that there exist quadratic Cremer Julia sets of positive area such that for a full Lebesgue measure set of angles the impressions are degenerate, the Julia set is connected im kleinen at the landing points of these rays, and these points are contained in no other impr...
متن کامل