Functional Analysis and Thermodynamic Formalism of Countable Shift Spaces

Tushar Das; Giulio Tiozzo; Mariusz Urbański; Anna Zdunik

Book

Functional Analysis and Thermodynamic Formalism of Countable Shift Spaces

, , and

Part of the multi-volume work

Open Dynamical Systems

Language: English

Published/Copyright: 2026

Published by

Become an author with De Gruyter Brill

Explore this Subject How to publish with us

This book is in the series

De Gruyter Expositions in Mathematics

About this book

Using the full power of countable alphabet thermodynamic formalism and modern functional analysis, the book presents a systematic treatment of the perturbative approach to open dynamical systems, covering those generated by a large class of naturally occurring holes through which the dynamical medium escapes. It highlights escape rates, conditionally invariant measures, surviving equilibrium states, and Hausdorff dimension of surviving sets.

Breaks new ground and contains original research advances.
Provides a compact yet self-contained account of material needed from functional analysis.
Discusses the powerful approach of singular perturbations.

Author / Editor information

M. Urbański, U of North Texas; T. Das, U of Wisconsin, USA; G. Tiozzo, U of Toronto, Canada; A. Zdunik, U of Warsaw, Poland.

Topics

Publicly Available

Frontmatter
I

Download PDF
Requires Authentication Unlicensed

Licensed

Dedication
V

Download PDF
Publicly Available

Contents
VII

Download PDF
Requires Authentication Unlicensed

Licensed

Preface
XIII

Download PDF
Requires Authentication Unlicensed

Licensed

Introduction to Volume 1
XXVII

Download PDF
Part I
Requires Authentication Unlicensed

Licensed

Selected topics from functional analysis
2

Download PDF
Requires Authentication Unlicensed

Licensed

1 Riesz functional calculus, spectrum, and perturbations of bounded linear operators
5

Download PDF
Requires Authentication Unlicensed

Licensed

2 Essential spectral radius, essential spectra, quasicompact operators, and spectral (D-)gaps
115

Download PDF
Requires Authentication Unlicensed

Licensed

3 Standard and nonstandard real and positive operators: Foundations and spectral properties
171

Download PDF
Requires Authentication Unlicensed

Licensed

4 Keller–Liverani perturbation theorem and its spectral consequences
277

Download PDF
Requires Authentication Unlicensed

Licensed

5 Short miscellaneous topics
363

Download PDF
Part II
Requires Authentication Unlicensed

Licensed

Thermodynamic formalism for countable alphabet symbolic dynamics
370

Download PDF
Requires Authentication Unlicensed

Licensed

6 Countable alphabet symbolic dynamics
375

Download PDF
Requires Authentication Unlicensed

Licensed

7 Thermodynamic formalism for acceptable potentials
379

Download PDF
Requires Authentication Unlicensed

Licensed

8 Perron–Frobenius operators induced by acceptable summable potentials; the dual operator and its eigenmeasures
397

Download PDF
Requires Authentication Unlicensed

Licensed

9 Hölder continuous functions
419

Download PDF
Requires Authentication Unlicensed

Licensed

10 Perron–Frobenius operators induced by finitely irreducible or finitely primitive subshifts and 1-cylinder Hölder continuous summable potentials: Spectral properties
434

Download PDF
Requires Authentication Unlicensed

Licensed

11 Gibbs states for finitely irreducible countable alphabet subshifts and 1-cylinder Hölder continuous summable potentials
462

Download PDF
Requires Authentication Unlicensed

Licensed

12 Equilibrium states for finitely irreducible countable alphabet subshifts and 1-cylinder Hölder continuous summable potentials: Existence, uniqueness, and Gibbs property
468

Download PDF
Requires Authentication Unlicensed

Licensed

13 Further properties of Gibbs/equilibrium states
477

Download PDF
Requires Authentication Unlicensed

Licensed

Bibliography

Download PDF
Requires Authentication Unlicensed

Licensed

Index
495

Download PDF

Publishing information

Pages and Images/Illustrations in book

eBook published on:

March 17, 2026

eBook ISBN:

9783111034270

Hardcover published on:

March 17, 2026

Hardcover ISBN:

9783111034157

Pages and Images/Illustrations in book

Front matter:

34

Main content:

502

Illustrations:

1

https://doi.org/10.1515/9783111034270

eBook ISBN: 9783111034270

Hardcover ISBN: 9783111034157

Keywords for this book

Dynamical systems; eigenvalues. functional analysis; singular perturbation; thermodynamic formalism

Audience(s) for this book

Libraries, graduate students, and researchers studying dynamical systems.

Safety & product resources

Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com

Functional Analysis and Thermodynamic Formalism of Countable Shift Spaces

Overview

About this book

Author / Editor information

Topics

Table of contents

Frontmatter

Dedication

Contents

Preface

Introduction to Volume 1

Selected topics from functional analysis

1 Riesz functional calculus, spectrum, and perturbations of bounded linear operators

2 Essential spectral radius, essential spectra, quasicompact operators, and spectral (D-)gaps

3 Standard and nonstandard real and positive operators: Foundations and spectral properties

4 Keller–Liverani perturbation theorem and its spectral consequences

5 Short miscellaneous topics

Thermodynamic formalism for countable alphabet symbolic dynamics

6 Countable alphabet symbolic dynamics

7 Thermodynamic formalism for acceptable potentials

8 Perron–Frobenius operators induced by acceptable summable potentials; the dual operator and its eigenmeasures

9 Hölder continuous functions

10 Perron–Frobenius operators induced by finitely irreducible or finitely primitive subshifts and 1-cylinder Hölder continuous summable potentials: Spectral properties

11 Gibbs states for finitely irreducible countable alphabet subshifts and 1-cylinder Hölder continuous summable potentials

12 Equilibrium states for finitely irreducible countable alphabet subshifts and 1-cylinder Hölder continuous summable potentials: Existence, uniqueness, and Gibbs property

13 Further properties of Gibbs/equilibrium states

Bibliography

Index

Bibliographic data