Dimensions of Sums with Self-similar Sets
نویسندگان
چکیده
For some self-similar sets K ⇢ R we obtain certain lower bounds for the lower Minkowski dimension of K + E in terms of the lower Minkowski dimension of E.
منابع مشابه
Continuity of Subadditive Pressure for Self-affine Sets
A certain ‘pressure’ functional Φ(T1, . . . , TN ), defined as the limit of sums of singular value functions of products of linear mappings (T1, . . . , TN ), is central in analysing fractal dimensions of self-affine sets. We investigate the continuity of Φ with respect to the linear mappings (T1, . . . , TN ) which underlie the self-affine sets.
متن کاملUniquely Remotal Sets in $c_0$-sums and $ell^infty$-sums of Fuzzy Normed Spaces
Let $(X, N)$ be a fuzzy normed space and $A$ be a fuzzy boundedsubset of $X$. We define fuzzy $ell^infty$-sums and fuzzy $c_0$-sums offuzzy normed spaces. Then we will show that in these spaces, all fuzzyuniquely remotal sets are singletons.
متن کاملThe fractal geometry of ancient Maya settlement
Ancient Maya settlement patterns exhibit fractal geometry both within communities and across regions. Fractals are self-similar sets of fractional dimension. In this paper, we show how Maya settlement patterns are logically and statistically self-similar. We demonstrate how to measure the fractal dimensions (or Hausdorff–Besicovitch dimensions) of several data sets. We describe nonlinear dynami...
متن کاملRandom fractal strings: their zeta functions, complex dimensions and spectral asymptotics
In this paper a string is a sequence of positive non-increasing real numbers which sums to one. For our purposes a fractal string is a string formed from the lengths of removed sub-intervals created by a recursive decomposition of the unit interval. By using the so called complex dimensions of the string, the poles of an associated zeta function, it is possible to obtain detailed information ab...
متن کاملFe b 20 02 GROWTH OF SELF - SIMILAR GRAPHS
Geometric properties of self-similar graphs concerning their volume growth and distances in certain finite subgraphs are discussed. The length scaling factor ν and the volume scaling factor µ can be defined similarly to the corresponding parameters of continuous self-similar sets. There are different notions of growth dimensions of graphs. For a rather general class of self-similar graphs it is...
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 2015