Pairs of periodic orbits with fixed homology difference
Morten S. Risager, Richard Sharp
TL;DR
This paper derives an asymptotic formula for counting pairs of closed orbits in a weak-mixing transitive Anosov flow with a specified homology difference, advancing understanding of orbit pair distributions.
Contribution
It introduces a new asymptotic counting formula for pairs of closed orbits with fixed homology difference in Anosov flows, a novel result in dynamical systems.
Findings
Established an asymptotic count for orbit pairs with fixed homology difference
Extended the understanding of orbit distribution in Anosov flows
Provided mathematical tools for analyzing homology classes in dynamical systems
Abstract
We obtain an asymptotic formula for the number of pairs of closed orbits of a weak-mixing transitive Anosov flow whose homology classes have a fixed difference.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · advanced mathematical theories · Stochastic processes and statistical mechanics