On Relative Category and Morse Decompositions for Infinite-Dimensional Dynamical Systems
Abstract
We employ the relative category to develop relations between the Wa\.zewski pair (N,E) and the Morse decomposition of the maximal invariant set in N 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.
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