For star-shaped domains, S¹-equivariant spectral invariants are bounded in positive characteristic, filtered symplectic homology dimension is bounded for pseudo-rotations, and non-degenerate Reeb flows with a negative mean index orbit have infinitely many prime closed orbits.
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Filtered Symplectic Homology and Closed Reeb Orbits
For star-shaped domains, S¹-equivariant spectral invariants are bounded in positive characteristic, filtered symplectic homology dimension is bounded for pseudo-rotations, and non-degenerate Reeb flows with a negative mean index orbit have infinitely many prime closed orbits.