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Combinatorial Constructions in Ergodic Theory and Dynamics
 
Anatole Katok Pennsylvania State University, University Park, PA
Combinatorial Constructions in Ergodic Theory and Dynamics
Softcover ISBN:  978-0-8218-3496-1
Product Code:  ULECT/30
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $55.20
eBook ISBN:  978-1-4704-2175-5
Product Code:  ULECT/30.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
Softcover ISBN:  978-0-8218-3496-1
eBook: ISBN:  978-1-4704-2175-5
Product Code:  ULECT/30.B
List Price: $134.00 $101.50
MAA Member Price: $120.60 $91.35
AMS Member Price: $107.20 $81.20
Combinatorial Constructions in Ergodic Theory and Dynamics
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Combinatorial Constructions in Ergodic Theory and Dynamics
Anatole Katok Pennsylvania State University, University Park, PA
Softcover ISBN:  978-0-8218-3496-1
Product Code:  ULECT/30
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $55.20
eBook ISBN:  978-1-4704-2175-5
Product Code:  ULECT/30.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
Softcover ISBN:  978-0-8218-3496-1
eBook ISBN:  978-1-4704-2175-5
Product Code:  ULECT/30.B
List Price: $134.00 $101.50
MAA Member Price: $120.60 $91.35
AMS Member Price: $107.20 $81.20
  • Book Details
     
     
    University Lecture Series
    Volume: 302003; 121 pp
    MSC: Primary 37;

    Ergodic theory studies measure-preserving transformations of measure spaces. These objects are intrinsically infinite, and the notion of an individual point or of an orbit makes no sense. Still there are a variety of situations when a measure-preserving transformation (and its asymptotic behavior) can be well described as a limit of certain finite objects (periodic processes).

    The first part of this book develops this idea systematically. Genericity of approximation in various categories is explored, and numerous applications are presented, including spectral multiplicity and properties of the maximal spectral type. The second part of the book contains a treatment of various constructions of cohomological nature with an emphasis on obtaining interesting asymptotic behavior from approximate pictures at different time scales.

    The book presents a view of ergodic theory not found in other expository sources. It is suitable for graduate students familiar with measure theory and basic functional analysis.

    Readership

    Graduate students and research mathematicians interested in ergodic theory.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Part I. Approximation and genericity in ergodic theory
    • 3. Part II. Cocycles, cohomology and combinatorial constructions
  • Additional Material
     
     
  • Reviews
     
     
    • For more advanced readers, however, this volume will be highly rewarding: they will be learning from a master of the subject, presenting some of his tools.

      Mathematical Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 302003; 121 pp
MSC: Primary 37;

Ergodic theory studies measure-preserving transformations of measure spaces. These objects are intrinsically infinite, and the notion of an individual point or of an orbit makes no sense. Still there are a variety of situations when a measure-preserving transformation (and its asymptotic behavior) can be well described as a limit of certain finite objects (periodic processes).

The first part of this book develops this idea systematically. Genericity of approximation in various categories is explored, and numerous applications are presented, including spectral multiplicity and properties of the maximal spectral type. The second part of the book contains a treatment of various constructions of cohomological nature with an emphasis on obtaining interesting asymptotic behavior from approximate pictures at different time scales.

The book presents a view of ergodic theory not found in other expository sources. It is suitable for graduate students familiar with measure theory and basic functional analysis.

Readership

Graduate students and research mathematicians interested in ergodic theory.

  • Chapters
  • 1. Introduction
  • 2. Part I. Approximation and genericity in ergodic theory
  • 3. Part II. Cocycles, cohomology and combinatorial constructions
  • For more advanced readers, however, this volume will be highly rewarding: they will be learning from a master of the subject, presenting some of his tools.

    Mathematical Reviews
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.