LEADER 03614nam 2200577 450 001 996495167503316 005 20230421132438.0 010 $a3-031-12031-0 035 $a(MiAaPQ)EBC7127696 035 $a(Au-PeEL)EBL7127696 035 $a(CKB)25219360800041 035 $a(PPN)265856167 035 $a(EXLCZ)9925219360800041 100 $a20230316d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGromov-Hausdorff stability of dynamical systems and applications to PDEs /$fJihoon Lee and Carlos Morales 210 1$aCham, Switzerland :$cBirkha?user,$d[2022] 210 4$dŠ2022 215 $a1 online resource (169 pages) 225 1 $aFrontiers in mathematics 311 08$aPrint version: Lee, Jihoon Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs Cham : Springer International Publishing AG,c2023 9783031120305 320 $aIncludes bibliographical references. 327 $aIntro -- Preface -- Contents -- Part I Abstract Theory -- 1 Gromov-Hausdorff Distances -- 1.1 Introduction -- 1.2 Preliminary Facts -- 1.3 Gromov-Hausdorff Distance for Metric Spaces -- 1.4 Precompactness, Completeness, and a Variational Principle -- 1.5 A Variational Principle for the Gromov-Hausdorff Distance -- 1.6 Distances Characterizing Homeomorphic Spaces -- 1.7 C0-Gromov-Hausdorff Distance for Dynamical Systems -- 1.8 Gromov-Hausdorff Space of Continuous Maps -- Exercises -- 2 Stability -- 2.1 Introduction -- 2.2 Definitions and Statement of Main Results -- 2.3 Proof of Theorem 2.1 -- 2.4 Isometric Stability: Proof of Theorem 2.4 -- 2.5 Proof of Theorem 2.5 -- 2.6 Gromov-Hausdorff Stability for Group Actions -- 2.7 Gromov-Hausdorff Stability of Global Attractors -- Exercises -- 3 Continuity of the Shift Operator -- 3.1 Introduction -- 3.2 Preliminary Facts -- 3.3 Proof of Theorem 3.1 -- 3.4 Application to Stability Theory -- Exercises -- 4 Shadowing from the Gromov-Hausdorff Viewpoint -- 4.1 Introduction -- 4.2 Definitions, Statement of Main Results, and Proofs -- Exercises -- Part II Applications to PDEs -- Introduction -- 5 GH-Stability of Reaction-Diffusion Equations -- 5.1 Introduction -- 5.2 Proof of Theorem 5.1 -- 5.3 Proof of Theorem 5.2 -- 6 Stability of Inertial Manifolds -- 6.1 Introduction -- 6.2 Proof of Theorem 6.2 -- 6.3 Proof of Theorem 6.3 -- 7 Stability of Chafee-Infante Equations -- 7.1 Introduction -- 7.2 L-Morse-Smale and Equivalence of Global Attractors -- 7.3 Continuity of Global Attractors -- 7.4 Geometric Stability -- References. 410 0$aFrontiers in mathematics. 606 $aDifferentiable dynamical systems 606 $aDifferential equations, Partial 606 $aGeometry, Differential 606 $aSistemes dināmics diferenciables$2thub 606 $aEquacions en derivades parcials$2thub 606 $aGeometria diferencial$2thub 608 $aLlibres electrōnics$2thub 615 0$aDifferentiable dynamical systems. 615 0$aDifferential equations, Partial. 615 0$aGeometry, Differential. 615 7$aSistemes dināmics diferenciables 615 7$aEquacions en derivades parcials 615 7$aGeometria diferencial 676 $a515.352 700 $aLee$b Jihoon$01263810 702 $aRojas$b Carlos Arnoldo Morales 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996495167503316 996 $aGromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs$92962669 997 $aUNISA