The Topological Dynamics of Ellis Actions

Buch | Softcover

152 Seiten

2008
American Mathematical Society (Verlag)
978-0-8218-4188-4 (ISBN)

Titel ist leider vergriffen;
keine Neuauflage

Artikel merken

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.

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

Erscheint lt. Verlag	30.12.2008
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-8218-4188-2 / 0821841882
ISBN-13	978-0-8218-4188-4 / 9780821841884
Zustand	Neuware