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Groups and topological dynamics / Volodymyr Nekrashevych.

By: Material type: TextTextSeries: Graduate studies in mathematics ; v. 223.Publisher: Providence, Rhode Island : American Mathematical Society, [2022]Copyright date: ©2022Description: xii, 693 pages : illustrations ; 26 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 9781470471200
  • 1470471205
  • 9781470463809
  • 1470463806
Subject(s): DDC classification:
  • 512.23 N418g
Other classification:
  • 20F69 | 20L05 | 37B05 | 37B10 | 37D20 | 37F15 | 20B27 | 20E32 | 20F50 | 37F20
Contents:
Dynamical systems -- Group actions -- Groupoids -- Iterated monodromy groups -- Groups from groupoids -- Growth and amenability.
Summary: This book is devoted to group-theoretic aspects of topological dynamics such as studying groups using their actions on topological spaces, using group theory to study symbolic dynamics, and other connections between group theory and dynamical systems. One of the main applications of this approach to group theory is the study of asymptotic properties of groups such as growth and amenability. The book presents recently developed techniques of studying groups of dynamical origin using the structure of their orbits and associated groupoids of germs, applications of the iterated monodromy groups to hyperbolic dynamical systems, topological full groups and their properties, amenable groups, groups of intermediate growth, and other topics. The book is suitable for graduate students and researchers interested in group theory, transformations defined by automata, topological and holomorphic dynamics, and theory of topological groupoids. Each chapter is supplemented by exercises of various levels of complexity. - Publisher
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Holdings
Item type Current library Collection Call number Copy number Status Date due Barcode
Books Books Castorina Livros (Books) 512.23 N418g 2022 IMPA (Browse shelf(Opens below)) 1 Available 39063000807962

Includes bibliographical references and index.

Dynamical systems -- Group actions -- Groupoids -- Iterated monodromy groups -- Groups from groupoids -- Growth and amenability.

This book is devoted to group-theoretic aspects of topological dynamics such as studying groups using their actions on topological spaces, using group theory to study symbolic dynamics, and other connections between group theory and dynamical systems. One of the main applications of this approach to group theory is the study of asymptotic properties of groups such as growth and amenability. The book presents recently developed techniques of studying groups of dynamical origin using the structure of their orbits and associated groupoids of germs, applications of the iterated monodromy groups to hyperbolic dynamical systems, topological full groups and their properties, amenable groups, groups of intermediate growth, and other topics. The book is suitable for graduate students and researchers interested in group theory, transformations defined by automata, topological and holomorphic dynamics, and theory of topological groupoids. Each chapter is supplemented by exercises of various levels of complexity. - Publisher

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