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

Linked to FindBook

Google Book

Amazon

博客來

Spectra and normal forms

Record Type:	Electronic resources : Monograph/item
Title/Author:	Spectra and normal forms/ by Luís Barreira, Claudia Valls.
Author:	Barreira, Luís.
other author:	Valls, Claudia.
Published:	Cham :Springer Nature Switzerland : : 2024.,
Description:	x, 133 p. :ill., digital ;24 cm.
[NT 15003449]:	Preface -- 1. Spectra and Examples -- 2. Asymptotic Behavior -- 3. Resonances and Normal Forms -- 4. Parameter-Dependent Dynamics -- 5. The Case of Differential Equations -- 6. Infinite-Dimensional Dynamics -- 7. Stable and Unstable Foliations -- 8. Construction of Smooth Conjugacies -- References.
Contained By:	Springer Nature eBook
Subject:	Spectral theory (Mathematics) -
Online resource:	https://doi.org/10.1007/978-3-031-51897-3
ISBN:	9783031518973

Spectra and normal forms
Barreira, Luís.

Spectra and normal forms[electronic resource] /by Luís Barreira, Claudia Valls. - Cham :Springer Nature Switzerland :2024. - x, 133 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8201. - SpringerBriefs in mathematics..

Preface -- 1. Spectra and Examples -- 2. Asymptotic Behavior -- 3. Resonances and Normal Forms -- 4. Parameter-Dependent Dynamics -- 5. The Case of Differential Equations -- 6. Infinite-Dimensional Dynamics -- 7. Stable and Unstable Foliations -- 8. Construction of Smooth Conjugacies -- References.

This book presents the reader with a streamlined exposition of the notions and results leading to the construction of normal forms and, ultimately, to the construction of smooth conjugacies for the perturbations of tempered exponential dichotomies. These are exponential dichotomies for which the exponential growth rates of the underlying linear dynamics never vanish. In other words, its Lyapunov exponents are all nonzero. The authors consider mostly difference equations, although they also briefly consider the case of differential equations. The content is self-contained and all proofs have been simplified or even rewritten on purpose for the book so that all is as streamlined as possible. Moreover, all chapters are supplemented by detailed notes discussing the origins of the notions and results as well as their proofs, together with the discussion of the proper context, also with references to precursor results and further developments. A useful chapter dependence chart is included in the Preface. The book is aimed at researchers and graduate students who wish to have a sufficiently broad view of the area, without the discussion of accessory material. It can also be used as a basis for graduate courses on spectra, normal forms, and smooth conjugacies. The main components of the exposition are tempered spectra, normal forms, and smooth conjugacies. The first two lie at the core of the theory and have an importance that undoubtedly surpasses the construction of conjugacies. Indeed, the theory is very rich and developed in various directions that are also of interest by themselves. This includes the study of dynamics with discrete and continuous time, of dynamics in finite and infinite-dimensional spaces, as well as of dynamics depending on a parameter. This led the authors to make an exposition not only of tempered spectra and subsequently of normal forms, but also briefly of some important developments in those other directions. Afterwards the discussion continues with the construction of stable and unstable invariant manifolds and, consequently, of smooth conjugacies, while using most of the former material. The notion of tempered spectrum is naturally adapted to the study of nonautonomous dynamics. The reason for this is that any autonomous linear dynamics with a tempered exponential dichotomy has automatically a uniform exponential dichotomy. Most notably, the spectra defined in terms of tempered exponential dichotomies and uniform exponential dichotomies are distinct in general. More precisely, the tempered spectrum may be smaller, which causes that it may lead to less resonances and thus to simpler normal forms. Another important aspect is the need for Lyapunov norms in the study of exponentially decaying perturbations and in the study of parameter-dependent dynamics. Other characteristics are the need for a spectral gap to obtain the regularity of the normal forms on a parameter and the need for a careful control of the small exponential terms in the construction of invariant manifolds and of smooth conjugacies.

ISBN: 9783031518973

Standard No.: 10.1007/978-3-031-51897-3doiSubjects--Topical Terms:

524915
Spectral theory (Mathematics)

LC Class. No.: QA320

Dewey Class. No.: 515.7222

Spectra and normal forms
LDR:04386nmm a2200337 a 4500 001 2369221
003 DE-He213
005 20240208141446.0
006 m d
007 cr nn 008maaau
008 241127s2024 sz s 0 eng d
020 $a 9783031518973 $q (electronic bk.)
020 $a 9783031518966 $q (paper)
024 7 $a 10.1007/978-3-031-51897-3 $2 doi
035 $a 978-3-031-51897-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA320
072 7 $a GPFC $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a GPFC $2 thema
082 0 4 $a 515.7222 $2 23
090 $a QA320 $b .B271 2024
100 1 $a Barreira, Luís. $3 3713732
245 1 0 $a Spectra and normal forms $h [electronic resource] / $c by Luís Barreira, Claudia Valls.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2024.
300 $a x, 133 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematics, $x 2191-8201
505 0 $a Preface -- 1. Spectra and Examples -- 2. Asymptotic Behavior -- 3. Resonances and Normal Forms -- 4. Parameter-Dependent Dynamics -- 5. The Case of Differential Equations -- 6. Infinite-Dimensional Dynamics -- 7. Stable and Unstable Foliations -- 8. Construction of Smooth Conjugacies -- References.
520 $a This book presents the reader with a streamlined exposition of the notions and results leading to the construction of normal forms and, ultimately, to the construction of smooth conjugacies for the perturbations of tempered exponential dichotomies. These are exponential dichotomies for which the exponential growth rates of the underlying linear dynamics never vanish. In other words, its Lyapunov exponents are all nonzero. The authors consider mostly difference equations, although they also briefly consider the case of differential equations. The content is self-contained and all proofs have been simplified or even rewritten on purpose for the book so that all is as streamlined as possible. Moreover, all chapters are supplemented by detailed notes discussing the origins of the notions and results as well as their proofs, together with the discussion of the proper context, also with references to precursor results and further developments. A useful chapter dependence chart is included in the Preface. The book is aimed at researchers and graduate students who wish to have a sufficiently broad view of the area, without the discussion of accessory material. It can also be used as a basis for graduate courses on spectra, normal forms, and smooth conjugacies. The main components of the exposition are tempered spectra, normal forms, and smooth conjugacies. The first two lie at the core of the theory and have an importance that undoubtedly surpasses the construction of conjugacies. Indeed, the theory is very rich and developed in various directions that are also of interest by themselves. This includes the study of dynamics with discrete and continuous time, of dynamics in finite and infinite-dimensional spaces, as well as of dynamics depending on a parameter. This led the authors to make an exposition not only of tempered spectra and subsequently of normal forms, but also briefly of some important developments in those other directions. Afterwards the discussion continues with the construction of stable and unstable invariant manifolds and, consequently, of smooth conjugacies, while using most of the former material. The notion of tempered spectrum is naturally adapted to the study of nonautonomous dynamics. The reason for this is that any autonomous linear dynamics with a tempered exponential dichotomy has automatically a uniform exponential dichotomy. Most notably, the spectra defined in terms of tempered exponential dichotomies and uniform exponential dichotomies are distinct in general. More precisely, the tempered spectrum may be smaller, which causes that it may lead to less resonances and thus to simpler normal forms. Another important aspect is the need for Lyapunov norms in the study of exponentially decaying perturbations and in the study of parameter-dependent dynamics. Other characteristics are the need for a spectral gap to obtain the regularity of the normal forms on a parameter and the need for a careful control of the small exponential terms in the construction of invariant manifolds and of smooth conjugacies.
650 0 $a Spectral theory (Mathematics) $3 524915
650 0 $a Perturbation (Mathematics) $3 518241
650 1 4 $a Dynamical Systems. $3 3538746
700 1 $a Valls, Claudia. $3 836483
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a SpringerBriefs in mathematics. $3 1566700
856 4 0 $u https://doi.org/10.1007/978-3-031-51897-3
950 $a Mathematics and Statistics (SpringerNature-11649)