Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs (Frontiers in Mathematics)

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.  

​Professor Lee got his PhD at Yonsei University in Seoul after receiving his bachelor's degree from the University of Washington in Seattle. He is Professor Morales Rojas got his PhD at IMPA, Rio de Janeiro, Brazil. He is currently Associated Professor at the Federal University of Rio de Janeiro, Brazil. His research interests include Dynamical Systems and its applications.