Constructs infinite-dimensional spaces of exact magnetic systems of strong geodesic type on closed manifolds, proving existence of null-homologous embedded periodic orbits with negative action below the strict Mañé critical value and hence non-contact type energy surfaces, resolving the conjecture.
Cristofaro-Gardiner, U
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Elementary spectral invariants simplify embedded contact homology spectral invariants for contact three-manifolds and can be used to prove some results on periodic orbits of Reeb vector fields, with the remaining results requiring the full ECH invariants.
citing papers explorer
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On the contact type conjecture for exact magnetic systems
Constructs infinite-dimensional spaces of exact magnetic systems of strong geodesic type on closed manifolds, proving existence of null-homologous embedded periodic orbits with negative action below the strict Mañé critical value and hence non-contact type energy surfaces, resolving the conjecture.
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Elementary spectral invariants and three-dimensional Reeb dynamics
Elementary spectral invariants simplify embedded contact homology spectral invariants for contact three-manifolds and can be used to prove some results on periodic orbits of Reeb vector fields, with the remaining results requiring the full ECH invariants.