Topological dynamics from a measure-theoretic viewpoint Keonhee Lee, Carlos Morales, Ngocthach Nguyen

Format:

Book

Author/Creator:

Lee, Keonhee, author.

Morales, Carlos, author.

Nguyen, Ngocthach, author.

Series:

Springer Asia Pacific mathematics series ; 3091-2563 v. 14

Springer Asia Pacific mathematics series 3091-2563 volume 14

Language:

English

Subjects (All):

Topological dynamics.

Physical Description:

1 online resource

Edition:

1st ed.

Place of Publication:

Singapore Springer [2026]

Summary:

This book introduces a new measurable perspective on dynamical systems by connecting concepts from topological dynamics with their measure-theoretic counterparts. A central theme is the translation of topological notions into measurable ones. For example, minimality in topological dynamics suggests a measurable analogue in ergodicity, where every invariant measurable set has either zero or full measure, offering an intuitive parallel between the two settings. Likewise, the notion of expansiveness is reinterpreted through expansive measures, in which almost all orbits separate beyond a fixed radius. These measurable analogues extend naturally to homeomorphisms and flows on compact metric spaces, which are explored in depth in Chapters 3 and 7. Building on this framework, the book develops measurable versions of several structural results from topological dynamics. Walters' stability theorem-grounded in shadowing, expansiveness, and topological stability-is revisited in Chapters 4 and 8 from a measurable perspective, while Smale's spectral decomposition theorem is reformulated in measurable terms in Chapters 5 and 9. By bridging topological and measurable viewpoints, the book offers a cohesive approach that provides new insights and directions for the study of dynamical systems

Contents:

Preliminaries

Topological Dynamics

Expansive Measures

Shadowing and Topological Stability

Measurable Spectral Decomposition

Topological Dynamics for Flows

Measure Expansiveness for Flows

Shadowing and Topological Stability for Flows

Measurable Spectral Decomposition for Flows

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (SpringerLink, viewed June 4, 2026)

ISBN:

9789819563906

9819563909

OCLC:

1593806343

Access Restriction:

Restricted for use by site license