Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs
Jihoon Lee, Carlos Morales
Springer International Publishing 
Naturwissenschaften, Medizin, Informatik, Technik / Analysis
Beschreibung
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.
Kundenbewertungen
Shift operator, Shadowing Property, Inertial Manifold, Stability of dynamical systems, Gromov-Hausdorff stability, Global Attractor, Gromov-Hausdorff distance