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

• Autore: Lee Jihoon
• Pubblicazione: Cham, Switzerland : , : Birkhäuser, , [2022]; ©2022
• Descrizione fisica: 1 online resource (169 pages)
• Disciplina: 515.352
• Soggetto topico: Differentiable dynamical systems; Differential equations, Partial; Geometry, Differential; Sistemes dinàmics diferenciables; Equacions en derivades parcials; Geometria diferencial
• Soggetto genere / forma: Llibres electrònics
• Persona (resp. second.): RojasCarlos Arnoldo Morales
• 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.
• Titolo autorizzato: Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs
• ISBN: 3-031-12031-0
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996495167503316
• Lo trovi qui: Univ. di Salerno
• Serie: Frontiers in mathematics.