The topological dynamics of Ellis actions
著者
書誌事項
The topological dynamics of Ellis actions
（Memoirs of the American Mathematical Society, no. 913）
American Mathematical Society, 2008
大学図書館所蔵 全12件
注記
Includes bibliographical references (p. 145-147) and index
内容説明・目次
内容説明
An Ellis semigroup is a compact space with a semigroup multiplication which is continuous in only one variable. An Ellis action is an action of an Ellis semigroup on a compact space such that for each point in the space the evaluation map from the semigroup to the space is continuous. At first the weak linkage between the topology and the algebra discourages expectations that such structures will have much utility. However, Ellis has demonstrated that these actions arise naturally from classical topological actions of locally compact groups on compact spaces and provide a useful tool for the study of such actions. In fact, via the apparatus of the enveloping semigroup the classical theory of topological dynamics is subsumed by the theory of Ellis actions. The authors' exposition describes and extends Ellis' theory and demonstrates its usefulness by unifying many recently introduced concepts related to proximality and distality. Moreover, this approach leads to several results which are new even in the classical setup.
目次
- Introduction
- Semigroups, monoids and their actions
- Ellis semigroups and Ellis actions
- Continuity conditions
- Applications using ideals
- Classical dynamical systems
- Classical actions: The group case
- Classical actions: The Abelian case
- Iterations of continuous maps
- Table
- Bibliography
- Index
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