Continuum-Wise Expansive Homeomorphisms

Kato, Hisao

Canadian journal of mathematics, Tome 45 (1993) no. 3, pp. 576-598

Résumé

The notion of expansive homeomorphism is important in topological dynamics and continuum theory. In this paper, a new kind of homeomorphism will be introduced and studied, namely the continuum-wise expansive homeomorphism. The class of continuum-wise expansive homeomorphisms is much larger than the one of expansive homeomorphisms. In fact, the class of continuum-wise expansive homeomorphisms contains many important homeomorphisms which often appear in "chaotic" topological dynamics and continuum theory, but which are not expansive homeomorphisms. For example, the shift maps of Knaster's indecomposable chainable continua are continuum-wise expansive homeomorphisms, but they are not expansive homeomorphisms. Also, there is a continuum-wise expansive homeomorphism on the pseudoarc. We study several properties of continuum-wise expansive homeomorphisms. Many theorems concerning expansive homeomorphisms will be generalized to the case of continuum-wise expansive homeomorphisms.

Détail

DOI : 10.4153/CJM-1993-030-4

Mots-clés : 54F50, 54B20, 54H20, 54B25, 58F15, expansive homeomorphism, inverse limit, shift map, sensitive dependence on inital conditions, topological entropy, tree-like, crooked, indecomposable

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