Weak separation properties for self-similar sets
نویسندگان
چکیده
منابع مشابه
Multifractal formalism for self-similar measures with weak separation condition
For any self-similar measure μ on R satisfying the weak separation condition, we show that there exists an open ball U0 with μ(U0) > 0 such that the distribution of μ, restricted on U0, is controlled by the products of a family of non-negative matrices, and hence μ|U0 satisfies a kind of quasi-product property. Furthermore, the multifractal formalism for μ|U0 is valid on the whole range of dime...
متن کاملSeparation Properties for Graph-Directed Self-Similar Fractals
Examples of “separation properties” for iterated function systems of similitudes include: the open set condition, the weak separation property, finite type. Alternate descriptions for these properties and relations among these properties have been worked out. Here we consider the same situation for “graph-directed” iterated function systems, and provide the definitions and proofs for that setti...
متن کاملSelf-Similar Solutions for Weak Shock Reflection
We present numerical solutions of a two-dimensional Riemann problem for the unsteady transonic small disturbance equations that provides an asymptotic description of the Mach reflection of weak shock waves. We develop a new numerical scheme to solve the equations in selfsimilar coordinates and use local grid refinement to resolve the solution in the reflection region. The solutions contain a re...
متن کاملOn univoque points for self-similar sets
Let K ⊆ R be the unique attractor of an iterated function system. We consider the case where K is an interval and study those elements of K with a unique coding. We prove under mild conditions that the set of points with a unique coding can be identified with a subshift of finite type. As a consequence of this, we can show that the set of points with a unique coding is a graph-directed selfsimi...
متن کاملStatistically Self - Similar Fractal Sets
In the present paper we define statistically self-similar sets, and, using a modification of method described in [2], [3], find a Hausdorff dimension of a statistically self-similar set.
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: Proceedings of the American Mathematical Society
سال: 1996
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-96-03527-7