1.

Record Nr.

UNISA996495167503316

Autore

Lee Jihoon

Titolo

Gromov-Hausdorff stability of dynamical systems and applications to PDEs / / Jihoon Lee and Carlos Morales

Pubbl/distr/stampa

Cham, Switzerland : , : Birkhäuser, , [2022]

©2022

ISBN

3-031-12031-0

Descrizione fisica

1 online resource (169 pages)

Collana

Frontiers in mathematics

Disciplina

515.352

Soggetti

Differentiable dynamical systems

Differential equations, Partial

Geometry, Differential

Sistemes dinàmics diferenciables

Equacions en derivades parcials

Geometria diferencial

Llibres electrònics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

Intro -- Preface -- Contents -- Part I Abstract Theory -- 1 Gromov-Hausdorff Distances -- 1.1 Introduction -- 1.2 Preliminary Facts -- 1.3 Gromov-Hausdorff Distance for Metric Spaces -- 1.4 Precompactness, Completeness, and a Variational Principle -- 1.5 A Variational Principle for the Gromov-Hausdorff Distance -- 1.6 Distances Characterizing Homeomorphic Spaces -- 1.7 C0-Gromov-Hausdorff Distance for Dynamical Systems -- 1.8 Gromov-Hausdorff Space of Continuous Maps -- Exercises -- 2 Stability -- 2.1 Introduction -- 2.2 Definitions and Statement of Main Results -- 2.3 Proof of Theorem 2.1 -- 2.4 Isometric Stability: Proof of Theorem 2.4 -- 2.5 Proof of Theorem 2.5 -- 2.6 Gromov-Hausdorff Stability for Group Actions -- 2.7 Gromov-Hausdorff Stability of Global Attractors -- Exercises -- 3 Continuity of the Shift Operator -- 3.1 Introduction -- 3.2 Preliminary Facts -- 3.3 Proof of Theorem 3.1 -- 3.4 Application to Stability Theory -- Exercises -- 4 Shadowing from the Gromov-Hausdorff Viewpoint -- 4.1 Introduction -- 4.2 Definitions, Statement of Main Results, and



Proofs -- Exercises -- Part II Applications to PDEs -- Introduction -- 5 GH-Stability of Reaction-Diffusion Equations -- 5.1 Introduction -- 5.2 Proof of Theorem 5.1 -- 5.3 Proof of Theorem 5.2 -- 6 Stability of Inertial Manifolds -- 6.1 Introduction -- 6.2 Proof of Theorem 6.2 -- 6.3 Proof of Theorem 6.3 -- 7 Stability of Chafee-Infante Equations -- 7.1 Introduction -- 7.2 L-Morse-Smale and Equivalence of Global Attractors -- 7.3 Continuity of Global Attractors -- 7.4 Geometric Stability -- References.