Connectivity Properties of Dimension Level Sets
نویسندگان
چکیده
منابع مشابه
Connectivity Properties of Dimension Level Sets
This paper initiates the study of sets in Euclidean space R (n ≥ 2) that are defined in terms of the dimensions of their elements. Specifically, given an interval I ⊆ [0, 1], we are interested in the connectivity properties of the set DIM consisting of all points in R whose (constructive Hausdorff) dimensions lie in the interval I. It is easy to see that the sets DIM and DIM(n−1,n] are totally ...
متن کاملConnectedness properties of dimension level sets
We prove that the set of all points of effective Hausdorff dimension 1 in Rn (n ≥ 2) is connected, and simultaneously that the complement of this set is not path-connected when n = 2.
متن کاملAlternated Julia Sets and Connectivity Properties
In this paper we present the alternated Julia sets, obtained by alternated iteration of two maps of the quadratic family 2 1 , 1,2 n n i z z c i and prove analytically and computationally that these sets can be connected, disconnected or totally disconnected verifying the known Fatou-Julia theorem in the case of polynomials of degree greater than two. A few examples are presented.
متن کاملConnectivity properties of Julia sets of Weierstrass elliptic functions
We discuss the connectivity properties of Julia sets of Weierstrass elliptic ℘ functions, accompanied by examples. We give sufficient conditions under which the Julia set is connected and show that triangular lattices satisfy this condition. We also give conditions under which the Fatou set of ℘ contains a toral band and provide an example of an order two elliptic function on a square lattice w...
متن کاملSome Properties of Lower Level-Sets of Convolutions
In the present paper we prove a certain lemma about the structure of “lower level-sets of convolutions”, which are sets of the form {x ∈ ZN : 1A ∗ 1A(x) ≤ γN} or of the form {x ∈ ZN : 1A ∗ 1A(x) < γN}, where A is a subset of ZN . One result we prove using this lemma is that if |A| = θN and |A + A| ≤ (1 − ε)N , 0 < ε < 1, then this level-set contains an arithmetic progression of length at least ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Notes in Theoretical Computer Science
سال: 2008
ISSN: 1571-0661
DOI: 10.1016/j.entcs.2008.03.022