On the structure of the intersection of two middle third Cantor sets.

Título inglés On the structure of the intersection of two middle third Cantor sets.
Título español Estructura de la intersección de dos conjuntos de Cantor de tercio central.
Autor/es Davis, Gregory J. ; Hu, Tian You
Organización Dep. Math. Univ. Wisconsin-Green Bay, Green Bay (Wisconsin), Estados Unidos
Revista 0214-1493
Publicación 1995, 39 (1): 43-60, 11 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés Motivated by the study of planar homoclinic bifurcations, in this paper we describe how the intersection of two middle third Cantor sets changes as the sets are translated across each other. The resulting description shows that the intersection is never empty; in fact, the intersection can be either finite or infinite in size. We show that when the intersection is finite then the number of points in the intersection will be either 2n or 3 · 2n. We also explore the Hausdorff dimension of the intersection of two middle third Cantor sets as the sets are translated across one another. We show that the Hausdorff dimension of the intersection can take on any value from 0 to ln 2 / ln 3; in addition, we show that for each Hausdorff dimension, between 0 and ln 2 / ln 3, there is a dense set of translation parameters for which the intersections have that particular Hausdorff dimension.
Clasificación UNESCO 120105
Palabras clave español Topología algebraica ; Dimensión de Hausdorff ; Sistemas dinámicos ; Sistemas no lineales ; Punto homoclínico ; Multiplicidad de intersección ; Teoría de bifurcación
Código MathReviews MR1336355
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