Intersections of Thick Cantor Sets
- ISBN-10
- 0821825283
- ISBN-13
- 9780821825280
- Category
- Bifurcation theory
- Pages
- 130
- Language
- English
- Published
- 1992
- Publisher
- American Mathematical Soc.
- Author
- Roger Kraft
Description
The concept of thickness assigns to every Cantor set in the real line a number from 0 to [infinity symbol]. It was known that for some pairs of numbers the intersection of Cantor sets with such numbers as thicknesses may be just one point and that, in some other cases, with certain conditions, the intersection must contain a Cantor set. The author gives a complete answer to the problem of determining all pairs of thicknesses for which the intersection may be a single point and all the pairs of thicknesses for which the intersection must contain a Cantor set. He also considers the problem of how often, as one Cantor set is being translated over another one, the intersection of the two Cantor sets contains a Cantor set.
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