On the relative category in the brake orbits problem - Corona, Dario; Giambò, Roberto; Giannoni, Fabio; Piccione, Paolo (Topological Methods in Nonlinear Analysis, 2023)
In this paper %dedicated to the memory of Edward Fadell and Sufian Husseiniwe show how the notion of the Lusternik-Schnirelmann relative category can be usedto study a multiplicity problem for brake orbits in a potential wellwhich is homeomorphic to the $N$-dimensional unit disk.The estimate of the relative category of the set of chords with endpoints on the$(N-1)$-unit sphere was shown to the third author byFadell and Husseini while he was visiting the University of Wisconsin at Madison.