Analysis on fractals, Laplacians on self-similar sets, noncommutative geometry and spectral dimensions
نویسندگان
چکیده
منابع مشابه
Self-similar fractals and arithmetic dynamics
The concept of self-similarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Self-similar fractals are subsets of algebraic varieties which can be written as a finite and disjoint union of `similar' copies. Fractals provide a framework in which, one can unite some results and conjectures in Diophantine g...
متن کاملDimensions of Points in Self-similar Fractals
Self-similar fractals arise as the unique attractors of iterated function systems (IFSs) consisting of finitely many contracting similarities satisfying an open set condition. Each point x in such a fractal F arising from an IFS S is naturally regarded as the “outcome” of an infinite coding sequence T (which need not be unique) over the alphabet Σk = {0, . . . , k − 1}, where k is the number of...
متن کاملFractals, coherent states and self-similarity induced noncommutative geometry∗
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the q-deformed algebra of coherent states. Self-similar structures are related to dissipation and to noncommutative geometry in the plane. The examples of the Koch curve and logarithmic spiral are considered in detail. It is suggested that the dynamical formation of fractals ...
متن کاملDecidability on Dube's Self-similar Fractals
Dube proved some undecidability on self-affine fractals. In this paper, we obtain the decidability for self-similar fractal of Dube’s type. In fact, we prove that the following problems are decidable to test if the Hausdorff dimension of a given Dube’s self-similar set is equal to its similarity dimension, and to test if a given Dube’s self-similar set satisfies the strong separation condition.
متن کاملDimensions of Sums with Self-similar Sets
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.
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: Topological Methods in Nonlinear Analysis
سال: 1994
ISSN: 1230-3429
DOI: 10.12775/tmna.1994.025