English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We introduce and study the barcode entropy for geodesic flows of closedRiemannian manifolds, which measures the exponential growth rate of the numberof 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 ofthe geodesic flow and, conversely, bounds from above the topological entropy ofany hyperbolic compact invariant set. As a consequence, for Riemannian metricson surfaces, the barcode entropy is equal to the topological entropy. A key tothe proofs and of independent interest is a crossing energy theorem forgradient flow lines of the energy functional.

Barcode entropy of geodesic flows