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Group Colorings and Bernoulli Subflows

Su Gao University of North Texas, Denton, TX
Steve Jackson University of North Texas, Denton, TX
Brandon Seward University of Michigan, Ann Arbor, MI
Available Formats:
Electronic ISBN: 978-1-4704-2875-4
Product Code: MEMO/241/1141.E
List Price: $101.00 MAA Member Price:$90.90
AMS Member Price: $60.60 Click above image for expanded view Group Colorings and Bernoulli Subflows Su Gao University of North Texas, Denton, TX Steve Jackson University of North Texas, Denton, TX Brandon Seward University of Michigan, Ann Arbor, MI Available Formats:  Electronic ISBN: 978-1-4704-2875-4 Product Code: MEMO/241/1141.E  List Price:$101.00 MAA Member Price: $90.90 AMS Member Price:$60.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 2412015; 241 pp
MSC: Primary 37; 20; Secondary 03;

In this paper the authors study the dynamics of Bernoulli flows and their subflows over general countable groups. One of the main themes of this paper is to establish the correspondence between the topological and the symbolic perspectives. From the topological perspective, the authors are particularly interested in free subflows (subflows in which every point has trivial stabilizer), minimal subflows, disjointness of subflows, and the problem of classifying subflows up to topological conjugacy. Their main tool to study free subflows will be the notion of hyper aperiodic points; a point is hyper aperiodic if the closure of its orbit is a free subflow.

• Chapters
• 1. Introduction
• 2. Preliminaries
• 3. Basic Constructions of $2$-Colorings
• 4. Marker Structures and Tilings
• 5. Blueprints and Fundamental Functions
• 6. Basic Applications of the Fundamental Method
• 7. Further Study of Fundamental Functions
• 8. The Descriptive Complexity of Sets of $2$-Colorings
• 9. The Complexity of the Topological Conjugacy Relation
• 10. Extending Partial Functions to $2$-Colorings
• 11. Further Questions
• Requests

Review Copy – for reviewers who would like to review an AMS book
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Accessibility – to request an alternate format of an AMS title
Volume: 2412015; 241 pp
MSC: Primary 37; 20; Secondary 03;

In this paper the authors study the dynamics of Bernoulli flows and their subflows over general countable groups. One of the main themes of this paper is to establish the correspondence between the topological and the symbolic perspectives. From the topological perspective, the authors are particularly interested in free subflows (subflows in which every point has trivial stabilizer), minimal subflows, disjointness of subflows, and the problem of classifying subflows up to topological conjugacy. Their main tool to study free subflows will be the notion of hyper aperiodic points; a point is hyper aperiodic if the closure of its orbit is a free subflow.

• Chapters
• 1. Introduction
• 2. Preliminaries
• 3. Basic Constructions of $2$-Colorings
• 4. Marker Structures and Tilings
• 5. Blueprints and Fundamental Functions
• 6. Basic Applications of the Fundamental Method
• 7. Further Study of Fundamental Functions
• 8. The Descriptive Complexity of Sets of $2$-Colorings
• 9. The Complexity of the Topological Conjugacy Relation
• 10. Extending Partial Functions to $2$-Colorings
• 11. Further Questions
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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