Legendrian persistence modules and dynamics

TL;DR

This paper connects persistence modules with Legendrian contact homology and Poisson invariants to demonstrate the existence of connecting trajectories in contact and symplectic dynamics.

Contribution

It introduces a novel framework linking persistence modules to contact and symplectic topology, enabling new dynamical existence results.

Findings

Establishes a relationship between persistence modules and Legendrian contact homology.

Proves the existence of connecting trajectories in Hamiltonian flows.

Links Poisson bracket invariants to topological methods.

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.