Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations [electronic resource] /

Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations [electronic resource] /

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This book presents a development of invariant manifold theory for a spe­ cific canonical nonlinear wave system -the perturbed nonlinear Schrooinger equation. The main results fall into two parts. The first part is concerned with the persistence and smoothness of locally invariant manifolds. The sec­ ond part is concerned with fibrations of the stable and unstable manifolds of inflowing and overflowing invariant manifolds. The central technique for proving these results is Hadamard's graph transform method generalized to an infinite-dimensional setting. However, our setting is somewhat different than other approaches to infinite dimensional invariant manifolds since for conservative wave equations many of the interesting invariant manifolds are infinite dimensional and noncom pact. The style of the book is that of providing very detailed proofs of theorems for a specific infinite dimensional dynamical system-the perturbed nonlinear Schrodinger equation. The book is organized as follows. Chapter one gives an introduction which surveys the state of the art of invariant manifold theory for infinite dimensional dynamical systems. Chapter two develops the general setup for the perturbed nonlinear Schrodinger equation. Chapter three gives the proofs of the main results on persistence and smoothness of invariant man­ ifolds. Chapter four gives the proofs of the main results on persistence and smoothness of fibrations of invariant manifolds. This book is an outgrowth of our work over the past nine years concerning homoclinic chaos in the perturbed nonlinear Schrodinger equation. The theorems in this book provide key building blocks for much of that work.

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Main Authors: Li, Charles. author., Wiggins, Stephen. author., SpringerLink (Online service)
Format: Texto biblioteca
Language:eng
Published: New York, NY : Springer New York : Imprint: Springer, 1997
Subjects:Mathematics., Mathematical analysis., Analysis (Mathematics)., Geometry., Manifolds (Mathematics)., Complex manifolds., Manifolds and Cell Complexes (incl. Diff.Topology)., Analysis.,
Online Access:http://dx.doi.org/10.1007/978-1-4612-1838-8
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id KOHA-OAI-TEST:191426
record_format koha
institution COLPOS
collection Koha
country México
countrycode MX
component Bibliográfico
access En linea
En linea
databasecode cat-colpos
tag biblioteca
region America del Norte
libraryname Departamento de documentación y biblioteca de COLPOS
language eng
topic Mathematics.
Mathematical analysis.
Analysis (Mathematics).
Geometry.
Manifolds (Mathematics).
Complex manifolds.
Mathematics.
Manifolds and Cell Complexes (incl. Diff.Topology).
Analysis.
Geometry.
Mathematics.
Mathematical analysis.
Analysis (Mathematics).
Geometry.
Manifolds (Mathematics).
Complex manifolds.
Mathematics.
Manifolds and Cell Complexes (incl. Diff.Topology).
Analysis.
Geometry.
spellingShingle Mathematics.
Mathematical analysis.
Analysis (Mathematics).
Geometry.
Manifolds (Mathematics).
Complex manifolds.
Mathematics.
Manifolds and Cell Complexes (incl. Diff.Topology).
Analysis.
Geometry.
Mathematics.
Mathematical analysis.
Analysis (Mathematics).
Geometry.
Manifolds (Mathematics).
Complex manifolds.
Mathematics.
Manifolds and Cell Complexes (incl. Diff.Topology).
Analysis.
Geometry.
Li, Charles. author.
Wiggins, Stephen. author.
SpringerLink (Online service)
Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations [electronic resource] /
description This book presents a development of invariant manifold theory for a spe­ cific canonical nonlinear wave system -the perturbed nonlinear Schrooinger equation. The main results fall into two parts. The first part is concerned with the persistence and smoothness of locally invariant manifolds. The sec­ ond part is concerned with fibrations of the stable and unstable manifolds of inflowing and overflowing invariant manifolds. The central technique for proving these results is Hadamard's graph transform method generalized to an infinite-dimensional setting. However, our setting is somewhat different than other approaches to infinite dimensional invariant manifolds since for conservative wave equations many of the interesting invariant manifolds are infinite dimensional and noncom pact. The style of the book is that of providing very detailed proofs of theorems for a specific infinite dimensional dynamical system-the perturbed nonlinear Schrodinger equation. The book is organized as follows. Chapter one gives an introduction which surveys the state of the art of invariant manifold theory for infinite dimensional dynamical systems. Chapter two develops the general setup for the perturbed nonlinear Schrodinger equation. Chapter three gives the proofs of the main results on persistence and smoothness of invariant man­ ifolds. Chapter four gives the proofs of the main results on persistence and smoothness of fibrations of invariant manifolds. This book is an outgrowth of our work over the past nine years concerning homoclinic chaos in the perturbed nonlinear Schrodinger equation. The theorems in this book provide key building blocks for much of that work.
format Texto
topic_facet Mathematics.
Mathematical analysis.
Analysis (Mathematics).
Geometry.
Manifolds (Mathematics).
Complex manifolds.
Mathematics.
Manifolds and Cell Complexes (incl. Diff.Topology).
Analysis.
Geometry.
author Li, Charles. author.
Wiggins, Stephen. author.
SpringerLink (Online service)
author_facet Li, Charles. author.
Wiggins, Stephen. author.
SpringerLink (Online service)
author_sort Li, Charles. author.
title Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations [electronic resource] /
title_short Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations [electronic resource] /
title_full Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations [electronic resource] /
title_fullStr Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations [electronic resource] /
title_full_unstemmed Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations [electronic resource] /
title_sort invariant manifolds and fibrations for perturbed nonlinear schrödinger equations [electronic resource] /
publisher New York, NY : Springer New York : Imprint: Springer,
publishDate 1997
url http://dx.doi.org/10.1007/978-1-4612-1838-8
work_keys_str_mv AT licharlesauthor invariantmanifoldsandfibrationsforperturbednonlinearschrodingerequationselectronicresource
AT wigginsstephenauthor invariantmanifoldsandfibrationsforperturbednonlinearschrodingerequationselectronicresource
AT springerlinkonlineservice invariantmanifoldsandfibrationsforperturbednonlinearschrodingerequationselectronicresource
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spelling KOHA-OAI-TEST:1914262018-07-30T23:15:32ZInvariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations [electronic resource] / Li, Charles. author. Wiggins, Stephen. author. SpringerLink (Online service) textNew York, NY : Springer New York : Imprint: Springer,1997.engThis book presents a development of invariant manifold theory for a spe­ cific canonical nonlinear wave system -the perturbed nonlinear Schrooinger equation. The main results fall into two parts. The first part is concerned with the persistence and smoothness of locally invariant manifolds. The sec­ ond part is concerned with fibrations of the stable and unstable manifolds of inflowing and overflowing invariant manifolds. The central technique for proving these results is Hadamard's graph transform method generalized to an infinite-dimensional setting. However, our setting is somewhat different than other approaches to infinite dimensional invariant manifolds since for conservative wave equations many of the interesting invariant manifolds are infinite dimensional and noncom pact. The style of the book is that of providing very detailed proofs of theorems for a specific infinite dimensional dynamical system-the perturbed nonlinear Schrodinger equation. The book is organized as follows. Chapter one gives an introduction which surveys the state of the art of invariant manifold theory for infinite dimensional dynamical systems. Chapter two develops the general setup for the perturbed nonlinear Schrodinger equation. Chapter three gives the proofs of the main results on persistence and smoothness of invariant man­ ifolds. Chapter four gives the proofs of the main results on persistence and smoothness of fibrations of invariant manifolds. This book is an outgrowth of our work over the past nine years concerning homoclinic chaos in the perturbed nonlinear Schrodinger equation. The theorems in this book provide key building blocks for much of that work.1 Introduction -- 1.1 Invariant Manifolds in Infinite Dimensions -- 1.2 Aims and Scope of This Monograph -- 2 The Perturbed Nonlinear Schrödinger Equation -- 2.1 The Setting for the Perturbed Nonlinear Schrödinger Equation -- 2.2 Spatially Independent Solutions: An Invariant Plane -- 2.3 Statement of the Persistence and Fiber Theorems -- 2.4 Explicit Representations for Invariant Manifolds and Fibers -- 2.5 Coordinates Centered on the Resonance Circle -- 2.6 (6 = 0) Invariant Manifolds and the Introduction of a Bump Function -- 3 Persistent Invariant Manifolds -- 3.1 Statement of the Persistence Theorem and the Strategy of Proof -- 3.2 Proof of the Persistence Theorems -- 3.3 The Existence of the Invariant Manifolds -- 3.4 Smoothness of the Invariant Manifolds -- 3.5 Completion of the Proof of the Proposition -- 4 Fibrations of the Persistent Invariant Manifolds -- 4.1 Statement of the Fiber Theorem and the Strategy of Proof -- 4.2 Rate Lemmas -- 4.3 The Existence of an Invariant Subbundle E -- 4.4 Smoothness of the Invariant Subbundle E -- 4.5 Existence of Fibers -- 4.6 Smoothness of the Fiber fE(Q) as a Submanifold -- 4.7 Metric Characterization of the Fibers -- 4.8 Smoothness of Fibers with Respect to the Base Point -- References.This book presents a development of invariant manifold theory for a spe­ cific canonical nonlinear wave system -the perturbed nonlinear Schrooinger equation. The main results fall into two parts. The first part is concerned with the persistence and smoothness of locally invariant manifolds. The sec­ ond part is concerned with fibrations of the stable and unstable manifolds of inflowing and overflowing invariant manifolds. The central technique for proving these results is Hadamard's graph transform method generalized to an infinite-dimensional setting. However, our setting is somewhat different than other approaches to infinite dimensional invariant manifolds since for conservative wave equations many of the interesting invariant manifolds are infinite dimensional and noncom pact. The style of the book is that of providing very detailed proofs of theorems for a specific infinite dimensional dynamical system-the perturbed nonlinear Schrodinger equation. The book is organized as follows. Chapter one gives an introduction which surveys the state of the art of invariant manifold theory for infinite dimensional dynamical systems. Chapter two develops the general setup for the perturbed nonlinear Schrodinger equation. Chapter three gives the proofs of the main results on persistence and smoothness of invariant man­ ifolds. Chapter four gives the proofs of the main results on persistence and smoothness of fibrations of invariant manifolds. This book is an outgrowth of our work over the past nine years concerning homoclinic chaos in the perturbed nonlinear Schrodinger equation. The theorems in this book provide key building blocks for much of that work.Mathematics.Mathematical analysis.Analysis (Mathematics).Geometry.Manifolds (Mathematics).Complex manifolds.Mathematics.Manifolds and Cell Complexes (incl. Diff.Topology).Analysis.Geometry.Springer eBookshttp://dx.doi.org/10.1007/978-1-4612-1838-8URN:ISBN:9781461218388

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