منابع مشابه
The Cantor Set
Analysis is the science of measure and optimization. As a collection of mathematical fields, it contains real and complex analysis, functional analysis, harmonic analysis and calculus of variations. Analysis has relations to calculus, geometry, topology, probability theory and dynamics. We will focus mostly on ”the geometry of fractals” today. Examples are Julia sets which belong to the subfiel...
متن کاملA Tame Cantor Set
A Cantor set is a non-empty, compact set that has neither interior nor isolated points. In this paper a Cantor set K ⊆ R is constructed such that every set definable in (R, <,+, ·,K) is Borel. In addition, we prove quantifierelimination and completeness results for (R, <,+, ·,K), making the set K the first example of a modeltheoretically tame Cantor set. This answers questions raised by Friedma...
متن کاملMinimal dynamical systems on the product of the Cantor set and the circle
We prove that a crossed product algebra arising from a minimal dynamical system on the product of the Cantor set and the circle has real rank zero if and only if that system is rigid. In the case that cocycles take values in the rotation group, it is also shown that rigidity implies tracial rank zero, and in particular, the crossed product algebra is isomorphic to a unital simple AT-algebra of ...
متن کاملDynamic Equations on the Cantor Set
In this paper we consider linear dynamic equations on Cantor ternary set. We derive an explicit formula for the solution of the associated initial value problem. In addition, we consider a special case in which the solution in question is given by a rather simple formula.
متن کاملMinimal dynamical systems on the product of the Cantor set and the circle II
Let X be the Cantor set and φ be a minimal homeomorphism on X×T. We show that the crossed product C∗-algebra C∗(X×T, φ) is a simple AT-algebra provided that the associated cocycle takes its values in rotations on T. Given two minimal systems (X × T, φ) and (Y × T, ψ) such that φ and ψ arise from cocycles with values in isometric homeomorphisms on T, we show that two systems are approximately K-...
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ژورنال
عنوان ژورنال: Tokyo Journal of Mathematics
سال: 1998
ISSN: 0387-3870
DOI: 10.3836/tjm/1270041997