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Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps
A Functional Approach
Buch von Viviane Baladi
Sprache: Englisch

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Beschreibung
The spectra of transfer operators associated to dynamical systems, when acting on suitable Banach spaces, contain key information about the ergodic properties of the systems. Focusing on expanding and hyperbolic maps, this book gives a self-contained account on the relation between zeroes of dynamical determinants, poles of dynamical zeta functions, and the discrete spectra of the transfer operators.

In the hyperbolic case, the first key step consists in constructing a suitable Banach space of anisotropic distributions. The first part of the book is devoted to the easier case of expanding endomorphisms, showing how the (isotropic) function spaces relevant there can be studied via Paley¿Littlewood decompositions, and allowing easier access to the construction of the anisotropic spaces which is performed in the second part.

This is the first book describing the use of anisotropic spaces in dynamics. Aimed at researchers and graduate students, it presents results and techniques developed since the beginning of the twenty-first century.
The spectra of transfer operators associated to dynamical systems, when acting on suitable Banach spaces, contain key information about the ergodic properties of the systems. Focusing on expanding and hyperbolic maps, this book gives a self-contained account on the relation between zeroes of dynamical determinants, poles of dynamical zeta functions, and the discrete spectra of the transfer operators.

In the hyperbolic case, the first key step consists in constructing a suitable Banach space of anisotropic distributions. The first part of the book is devoted to the easier case of expanding endomorphisms, showing how the (isotropic) function spaces relevant there can be studied via Paley¿Littlewood decompositions, and allowing easier access to the construction of the anisotropic spaces which is performed in the second part.

This is the first book describing the use of anisotropic spaces in dynamics. Aimed at researchers and graduate students, it presents results and techniques developed since the beginning of the twenty-first century.
Über den Autor
Viviane Baladi has been working as a researcher for CNRS since 1990 (currently Directeur de Recherche at Institut de Mathématiques de Jussieu-Paris Rive Gauche), spending several academic years on leave to teach at the Universities of Geneva and Copenhagen, and at the Eidgenössische Technische Hochschule Zürich. Her interest in dynamical zeta functions and transfer operators developed during her Ph.D. in Geneva. She has since applied transfer operators to algorithmics, linear response and the violation thereof, and rates of mixing for Sinai billiards. She has further played a key role introducing anisotropic spaces of distributions in dynamical systems.
Zusammenfassung

Collects recent results on transfer operators, anisotropic Banach spaces, and dynamical determinants of hyperbolic systems

Gives a self-contained account of proofs (some of them new) starting with the basic case of expanding maps for easier readability

Each chapter ends with a list of open research problems

Inhaltsverzeichnis
¿1 Introduction.- Part I Smooth expanding maps.- 2 Smooth expanding maps: The spectrum of the transfer operator.- 3 Smooth expanding maps: Dynamical determinants.- Part II Smooth hyperbolic maps.- 4 Anisotropic Banach spaces dened via cones.- 5 A variational formula for the essential spectral radius.- 6 Dynamical determinants for smooth hyperbolic dynamics.- 7 Two applications of anisotropic spaces.- Part III Appendices.- A Spectral theory.- B Thermodynamic formalism: Non-multiplicative topological pressure.- C Properly supported operators (pseudolocality).- D Alternative proofs for C1 dynamics and weights.- References.- Index.
Details
Erscheinungsjahr: 2018
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 308
Reihe: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Inhalt: xv
291 S.
1 s/w Illustr.
291 p. 1 illus.
ISBN-13: 9783319776606
ISBN-10: 3319776606
Sprache: Englisch
Herstellernummer: 978-3-319-77660-6
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Baladi, Viviane
Auflage: 1st ed. 2018
Hersteller: Springer International Publishing
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Maße: 241 x 160 x 22 mm
Von/Mit: Viviane Baladi
Erscheinungsdatum: 28.05.2018
Gewicht: 0,685 kg
preigu-id: 111333074
Über den Autor
Viviane Baladi has been working as a researcher for CNRS since 1990 (currently Directeur de Recherche at Institut de Mathématiques de Jussieu-Paris Rive Gauche), spending several academic years on leave to teach at the Universities of Geneva and Copenhagen, and at the Eidgenössische Technische Hochschule Zürich. Her interest in dynamical zeta functions and transfer operators developed during her Ph.D. in Geneva. She has since applied transfer operators to algorithmics, linear response and the violation thereof, and rates of mixing for Sinai billiards. She has further played a key role introducing anisotropic spaces of distributions in dynamical systems.
Zusammenfassung

Collects recent results on transfer operators, anisotropic Banach spaces, and dynamical determinants of hyperbolic systems

Gives a self-contained account of proofs (some of them new) starting with the basic case of expanding maps for easier readability

Each chapter ends with a list of open research problems

Inhaltsverzeichnis
¿1 Introduction.- Part I Smooth expanding maps.- 2 Smooth expanding maps: The spectrum of the transfer operator.- 3 Smooth expanding maps: Dynamical determinants.- Part II Smooth hyperbolic maps.- 4 Anisotropic Banach spaces dened via cones.- 5 A variational formula for the essential spectral radius.- 6 Dynamical determinants for smooth hyperbolic dynamics.- 7 Two applications of anisotropic spaces.- Part III Appendices.- A Spectral theory.- B Thermodynamic formalism: Non-multiplicative topological pressure.- C Properly supported operators (pseudolocality).- D Alternative proofs for C1 dynamics and weights.- References.- Index.
Details
Erscheinungsjahr: 2018
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 308
Reihe: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Inhalt: xv
291 S.
1 s/w Illustr.
291 p. 1 illus.
ISBN-13: 9783319776606
ISBN-10: 3319776606
Sprache: Englisch
Herstellernummer: 978-3-319-77660-6
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Baladi, Viviane
Auflage: 1st ed. 2018
Hersteller: Springer International Publishing
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Maße: 241 x 160 x 22 mm
Von/Mit: Viviane Baladi
Erscheinungsdatum: 28.05.2018
Gewicht: 0,685 kg
preigu-id: 111333074
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