Legendrian persistence modules and dynamics

Abstract

We relate the machinery of persistence modules to the Legendrian contact homology theory and to Poisson bracket invariants, and use it to show the existence of connecting trajectories of contact and symplectic Hamiltonian flows.

New steps in $C^0$ symplectic and contact geometry of smooth submanifolds

“…Theorem 7 (Theorem 1.5. in [EP21]). (i) Let ψ be a positive function on Q, and let Λ 1 := {z = ψ(q), p = ψ (q)} be the graph of its 1-jet.…”

“…Their proof relies on methods available only in the the 3-dimensional contact manifolds. On the other hand, the main tool for our proof is recent result of Entov and Polterovich [EP21] which includes the concept of contact interlinking of Legendrians, and it is available in higher dimensions as well. This is the first higher dimensional instance of the above question as stated.…”