2025/03/11 by Erol Barut, Barut, Erol, Viktor L. Ginzburg +1 · 1 voice · 2 citations
Mathematics · Physics and Astronomy · #37B40 #37J12 #37J55 #53D40 #Barcode #Exponential function #FOS: Mathematics #Hamiltonian mechanics #Hamiltonian system #Integrable system #Invariant (physics) #Polynomial #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG) #Symplectic geometry #math.SG
paper · pdf · doi:10.48550/arxiv.2503.08922
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/03/11 · arxiv published 2025/03/11 · arxiv updated 2025/03/11 · openalex created_date 2025/10/13 · openalex updated_date 2026/08/05
We continue investigating the connection between the dynamics of a Hamiltonian system and the barcode growth of the associated Floer or symplectic homology persistence module, focusing now on completely integrable systems. We show that for convex/concave or real analytic toric domains and convex/concave or real analytic completely integrable Hamiltonians on closed toric manifolds the barcode has polynomial growth with degree (i.e., slow barcode entropy) not exceeding half of the dimension. This slow polynomial growth contrasts with exponential growth for many systems with sufficiently non-trivial dynamics. We also touch upon the barcode growth function as an invariant of the interior of the domain and use it to distinguish some open domains.