Perfect Reeb flows and action-index relations
Abbreviated Journal Title
Periodic orbits; Contact forms; Reeb flows; Contact homology; COMPACT CONVEX HYPERSURFACES; SYMPLECTIC FIELD-THEORY; HAMILTONIAN; DIFFEOMORPHISMS; CLOSED CHARACTERISTICS; WEINSTEIN CONJECTURE; CONTACT; HOMOLOGY; PERIODIC POINTS; ENERGY SURFACES; MORSE-THEORY; DYNAMICS; Mathematics
We study non-degenerate Reeb flows arising from perfect contact forms, i.e., the forms with vanishing contact homology differential. In particular, we obtain upper bounds on the number of simple closed Reeb orbits for such forms on a variety of contact manifolds and certain action-index resonance relations for the standard contact sphere. Using these results, we reprove a theorem due to Bourgeois, Cieliebak and Ekholm characterizing perfect Reeb flows on the standard contact three-sphere as non-degenerate Reeb flows with exactly two simple closed orbits.
"Perfect Reeb flows and action-index relations" (2015). Faculty Bibliography 2010s. 6555.