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One point intersections of middle-α Cantor sets

Published online by Cambridge University Press:  19 September 2008

Roger L. Kraft
Roger L. Kraft
Affiliation:
Department of Mathematics, Computer Science, and Statistics, Purdue University-Calumet Hammond, IN 46323, USA
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Abstract

For α ∈ (0, 1), let Γα denote the middle-α Cantor set contained in the interval [0,1]. Let denote the set of all t∈[−1,1] such that Γα ∩(Γα+t)is a single point. Both a geometric and a symbolic description of each is presented. The symbolic description of each will be as a shift invariant subset of the one-sided two shift that is determined by inequalities. An equivalence relation is defined on the one-sided two shift and then a linear order relation is defined on the equivalence classes. This order relation on the equivalence classes describes how the sets shrink as a decreases from ⅓ to 0.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 14 , Issue 3 , September 1994 , pp. 537 - 549
Copyright
Copyright © Cambridge University Press 1994

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