東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Dynamical Zeta functions and dynamic...

Baladi, Viviane.

Linked to FindBook

Google Book

Amazon

博客來

Dynamical Zeta functions and dynamical determinants for hyperbolic maps = a functional approach /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Dynamical Zeta functions and dynamical determinants for hyperbolic maps/ by Viviane Baladi.
Reminder of title:	a functional approach /
Author:	Baladi, Viviane.
Published:	Cham :Springer International Publishing : : 2018.,
Description:	xv, 291 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Functions, Zeta. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-77661-3
ISBN:	9783319776613

Dynamical Zeta functions and dynamical determinants for hyperbolic maps = a functional approach /
Baladi, Viviane.

Dynamical Zeta functions and dynamical determinants for hyperbolic mapsa functional approach /[electronic resource] :by Viviane Baladi. - Cham :Springer International Publishing :2018. - xv, 291 p. :ill., digital ;24 cm. - Ergebnisse der mathematik und ihrer grenzgebiete. 3. folge / a series of modern surveys in mathematics,v.680071-1136 ;. - Ergebnisse der mathematik und ihrer grenzgebiete. 3. folge / a series of modern surveys in mathematics ;v.68..

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.

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.

ISBN: 9783319776613

Standard No.: 10.1007/978-3-319-77661-3doiSubjects--Topical Terms:

558393
Functions, Zeta.

LC Class. No.: QA351 / .B353 2018

Dewey Class. No.: 515.56

Dynamical Zeta functions and dynamical determinants for hyperbolic maps = a functional approach /
LDR:02821nmm a2200325 a 4500 001 2146211
003 DE-He213
005 20181130092826.0
006 m d
007 cr nn 008maaau
008 190227s2018 gw s 0 eng d
020 $a 9783319776613 $q (electronic bk.)
020 $a 9783319776606 $q (paper)
024 7 $a 10.1007/978-3-319-77661-3 $2 doi
035 $a 978-3-319-77661-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA351 $b .B353 2018
072 7 $a PBWR $2 bicssc
072 7 $a MAT034000 $2 bisacsh
082 0 4 $a 515.56 $2 23
090 $a QA351 $b .B171 2018
100 1 $a Baladi, Viviane. $3 3332572
245 1 0 $a Dynamical Zeta functions and dynamical determinants for hyperbolic maps $h [electronic resource] : $b a functional approach / $c by Viviane Baladi.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a xv, 291 p. : $b ill., digital ; $c 24 cm.
490 1 $a Ergebnisse der mathematik und ihrer grenzgebiete. 3. folge / a series of modern surveys in mathematics, $x 0071-1136 ; $v v.68
505 0 $a 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.
520 $a 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.
650 0 $a Functions, Zeta. $3 558393
650 0 $a Dynamics. $3 519830
650 0 $a Banach spaces. $3 579190
650 0 $a Geometry, Hyperbolic. $3 532067
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 891276
650 2 4 $a Functional Analysis. $3 893943
650 2 4 $a Operator Theory. $3 897311
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Ergebnisse der mathematik und ihrer grenzgebiete. 3. folge / a series of modern surveys in mathematics ; $v v.68. $3 3332573
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-77661-3
950 $a Mathematics and Statistics (Springer-11649)