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Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs
Authors: ---
ISBN: 9783031120312 9783031120305 9783031120329 Year: 2022 Publisher: Cham Springer International Publishing :Imprint: Birkhäuser

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Abstract

This monograph presents new insights into the perturbation theory of dynamical systems based on the Gromov-Hausdorff distance. In the first part, the authors introduce the notion of Gromov-Hausdorff distance between compact metric spaces, along with the corresponding distance for continuous maps, flows, and group actions on these spaces. They also focus on the stability of certain dynamical objects like shifts, global attractors, and inertial manifolds. Applications to dissipative PDEs, such as the reaction-diffusion and Chafee-Infante equations, are explored in the second part. This text will be of interest to graduates students and researchers working in the areas of topological dynamics and PDEs. .


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Gromov-Hausdorff stability of dynamical systems and applications to PDEs
Authors: ---
ISBN: 3031120302 3031120310 Year: 2022 Publisher: Cham, Switzerland : Birkhäuser,

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Keywords

Differentiable dynamical systems. --- Differential equations, Partial. --- Geometry, Differential. --- Sistemes dinàmics diferenciables --- Equacions en derivades parcials --- Geometria diferencial --- Geometria --- Càlcul de tensors --- Connexions (Matemàtica) --- Coordenades --- Corbes --- Cossos convexos --- Dominis convexos --- Espais de curvatura constant --- Espais simètrics --- Estructures hermitianes --- Formes diferencials --- G-estructures --- Geodèsiques (Matemàtica) --- Geometria de Riemann --- Geometria diferencial global --- Geometria integral --- Geometria simplèctica --- Hiperespai --- Subvarietats (Matemàtica) --- Topologia diferencial --- Varietats (Matemàtica) --- Varietats de Kähler --- EDPs --- Equació diferencial en derivades parcials --- Equacions diferencials en derivades parcials --- Equacions diferencials parcials --- Equacions diferencials --- Dispersió (Matemàtica) --- Equació d'ona --- Equació de Dirac --- Equació de Fokker-Planck --- Equació de Schrödinger --- Equacions de Navier-Stokes --- Equacions de Hamilton-Jacobi --- Equacions de Maxwell --- Equacions de Monge-Ampère --- Equacions de Von Kármán --- Equacions diferencials el·líptiques --- Equacions diferencials hiperbòliques --- Equacions diferencials parabòliques --- Equacions diferencials parcials estocàstiques --- Funcions harmòniques --- Laplacià --- Problema de Cauchy --- Problema de Neumann --- Teoria espectral (Matemàtica) --- Dinàmica diferencial --- Dinàmica combinatòria --- Exponents de Lyapunov --- Fluxos (Sistemes dinàmics diferenciables) --- Sistemes dinàmics aleatoris --- Sistemes dinàmics complexos --- Sistemes dinàmics hiperbòlics --- Sistemes hamiltonians --- Teoria de la bifurcació --- Dinàmica topològica --- Differential geometry --- Partial differential equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics

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