عنوان

Cantor minimal systems /

شابک

1470441152

شابک

9781470441159

عنوان اصلي

Cantor minimal systems /

نام عام مواد

[Book]

نام نخستين پديدآور

Ian F. Putnam.

محل نشرو پخش و غیره

Providence, Rhode Island :

نام ناشر، پخش کننده و غيره

American Mathematical Society,

تاریخ نشرو بخش و غیره

[2018]

نام خاص و کميت اثر

xiii, 149 pages :

ساير جزييات

illustrations ;

ابعاد

26 cm.

عنوان فروست

University lecture series ;

مشخصه جلد

volume 70

متن يادداشت

Includes bibliographical references and indexes.

متن يادداشت

Machine generated contents note: ch. 1 An example: A tale of two equivalence relations -- ch. 2 Basics: Cantor sets and orbit equivalence -- 1.Cantor sets -- 2.Orbit equivalence -- ch. 3 Bratteli diagrams: Generalizing the example -- ch. 4 The Bratteli-Vershik model: Generalizing the example -- ch. 5 The Bratteli-Vershik model: Completeness -- ch. 6 Etale equivalence relations: Unifying the examples -- 1.Local actions and etale equivalence relations -- 2.Re as an etale equivalence relation -- 3.Rq as an etale equivalence relation -- ch. 7 The D invariant -- 1.The group C(X, Z) -- 2.Ordered abelian groups -- 3.The invariant -- 4.Inductive limits of groups -- 5.The dimension group of a Bratteli diagram -- 6.The invariant for AF-equivalence relations -- 7.The invariant for Z-actions -- ch. 8 The Effros-Handelman-Shen Theorem -- 1.The statement -- 2.The proof -- ch. 9 The Bratteli-Elliott-Krieger Theorem -- ch. 10 Strong orbit equivalence -- 1.Orbit cocycles

متن يادداشت

Note continued: 2.Strong orbit equivalence and classification -- ch. 11 The Dm invariant -- 1.An innocent's guide to measure theory -- 2.States on ordered abelian groups -- 3.R-invariant measures -- 4.R-invariant measures and the D invariant -- 5.The invariant -- 6.The invariant for AF-equivalence relations -- 7.The invariant for Z-actions -- 8.The classification of odometers -- ch. 12 The absorption theorem -- 1.The simplest version -- 2.The proof -- 3.Matui's absorption theorem -- ch. 13 The classification of AF-equivalence relations -- 1.An example -- 2.The classification theorem -- ch. 14 The classification of $$-actions.

بدون عنوان

0

بدون عنوان

0

متن يادداشت

Within the subject of topological dynamics, there has been considerable recent interest in systems where the underlying topological space is a Cantor set. Such systems have an inherently combinatorial nature, and seminal ideas of Anatoly Vershik allowed for a combinatorial model, called the Bratteli-Vershik model, for such systems with no non-trivial closed invariant subsets. This model led to a construction of an ordered abelian group which is an algebraic invariant of the system providing a complete classification of such systems up to orbit equivalence. The goal of this book is to give a statement of this classification result and to develop ideas and techniques leading to it. Rather than being a comprehensive treatment of the area, this book is aimed at students and researchers trying to learn about some surprising connections between dynamics and algebra. The only background material needed is a basic course in group theory and and a basic course in general topology.

موضوع مستند نشده

Cantor sets.

موضوع مستند نشده

Compact spaces.

موضوع مستند نشده

Topological spaces.

موضوع مستند نشده

Cantor sets.

موضوع مستند نشده

Compact spaces.

موضوع مستند نشده

Dynamical systems and ergodic theory -- Topological dynamics -- Transformations and group actions with special properties (minimality, distality, proximality, etc.).

موضوع مستند نشده

Group theory and generalizations -- Special aspects of infinite or finite groups -- Ordered groups.

موضوع مستند نشده

Topological spaces.

شماره

ويراست

شماره رده

نشانه اثر

شماره رده

کد سيستم

مستند نام اشخاص تاييد نشده

Putnam, Ian F., (Ian Fraser),1958-

تاريخ عمليات

20200823025819.0

قواعد فهرست نويسي ( بخش توصيفي )

rda

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y