Intersections of thick Cantor sets
Author(s)
Bibliographic Information
Intersections of thick Cantor sets
（Memoirs of the American Mathematical Society, no. 468）
American Mathematical Society, 1992
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Note
"May 1992, volume 97, number 468 (second of 3 numbers)" -- T.p
Includes references
Description and Table of Contents
Description
Problems in dynamical systems involving homoclinic tangencies, homoclinic bifurcations, and the creation of horseshoes have led to the problem of analysing the difference sets ( t *G. ( *G' + t ) = 0) of Cantor sets *G and *G' embedded in the real line. In this work, the author proves two theorems about difference sets of Cantor sets, both of which involve the concept of the thickness of a Cantor set. The first gives conditions on the thicknesses of two Cantor sets that determine if the intersection of the two Cantor sets must contain a Cantor set or if the intersection may, in a nontrivial way, be as small as one point. The second theorem states that if the product of the thicknesses of two Cantor sets is strictly greater than one, then for a generic point t in their difference set, *G. ( *G' + t ) contains a Cantor set.
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