Barcode entropy of geodesic flows - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

Barcode entropy of geodesic flows

(1) , (2) , (3)
1
2
3

Abstract

We introduce and study the barcode entropy for geodesic flows of closed Riemannian manifolds, which measures the exponential growth rate of the number of not-too-short bars in the Morse-theoretic barcode of the energy functional. We prove that the barcode entropy bounds from below the topological entropy of the geodesic flow and, conversely, bounds from above the topological entropy of any hyperbolic compact invariant set. As a consequence, for Riemannian metrics on surfaces, the barcode entropy is equal to the topological entropy. A key to the proofs and of independent interest is a crossing energy theorem for gradient flow lines of the energy functional.

Dates and versions

ensl-03895619 , version 1 (13-12-2022)

Identifiers

Cite

Viktor L. Ginzburg, Basak Z. Gurel, Marco Mazzucchelli. Barcode entropy of geodesic flows. 2022. ⟨ensl-03895619⟩
0 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More