Nicht lieferbar
Intersections of Thick Cantor Sets
Versandkostenfrei!
Nicht lieferbar
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, b...
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.
Table of contents:
Theorems and examples; Cantor sets and thickness; Proof of Theorem 1.2; Third kind of overlapped point; Second kind of overlapped point; First kind of overlapped point; The dynamics of *V *t *t' ; Results about the geometric process; Proof of Theorem 6.2(1); The boundary between *L1 and *L2; Proof of Theorem 1.1.
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.
Table of contents:
Theorems and examples; Cantor sets and thickness; Proof of Theorem 1.2; Third kind of overlapped point; Second kind of overlapped point; First kind of overlapped point; The dynamics of *V *t *t' ; Results about the geometric process; Proof of Theorem 6.2(1); The boundary between *L1 and *L2; Proof of Theorem 1.1.
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.