On Relative Category and Morse Decompositions for Infinite-Dimensional Dynamical Systems
arXiv:1910.05002 · doi:10.1016/j.topol.2021.107624
Abstract
We employ the relative category to develop relations between the Ważewski pair and the Morse decomposition of the maximal invariant set in $\ol{N\sm E}$ for infinite-dimensional dynamical systems. Via these relations, we can detect connecting trajectories between Morse sets and obtain a dynamical-system version of critical point theorem with relative category.