2022/07/07 by Erman Çınelı, Cineli, Erman, Viktor L. Ginzburg +3 · 1 citation
Mathematics · Physics and Astronomy · #37J11 #37J46 #53D40 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2207.03613
openalex publication_date 2022/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is a follow up to the authors' recent work on barcode entropy. We study the growth of the barcode of the Floer complex for the iterates of a compactly supported Hamiltonian diffeomorphism. In particular, we introduce sequential barcode entropy which has properties similar to barcode entropy, bounds it from above and is more sensitive to the barcode growth. We prove that in dimension two the sequential barcode entropy equals the topological entropy and hence equals the ordinary barcode entropy. We also study the behavior of the γ-norm under iterations. We show that the γ-norm of the iterates is separated from zero when the map has sufficiently many hyperbolic periodic points and, as a consequence, it is separated from zero C^∞-generically in dimension two. We also touch upon properties of the barcode entropy of pseudo-rotations and, more generally, γ-almost periodic maps.