Anosov flows are the gold standard of chaotic dynamics: every orbit is hyperbolic, the flow is structurally stable, and the dynamics cannot be simplified. Constructing new Anosov flows on new manifolds is hard because the hyperbolicity condition is global — it must hold everywhere simultaneously.
The paper on new Anosov flows via bicontact structures (arXiv: 2603.22250) introduces a new construction method using hyperbolic plugs — local models that can be glued together.
A bicontact plug is a piece of a 3-manifold with boundary (a surface bundle over the circle) that carries two contact structures simultaneously. The bicontact condition — two contact forms whose wedge products have opposite signs — is the local signature of Anosov dynamics. The gluing theorem says that if the plugs match along their boundaries, the resulting closed manifold supports a transitive Anosov flow.
The method produces manifolds with many nonequivalent Anosov flows: toroidal manifolds from figure-eight knot complements can support numerous distinct Anosov dynamics. Generalized Handel–Thurston surgeries, previously abstract constructions, are realized concretely through sequences of Goodman–Fried surgeries.
The through-claim: global hyperbolicity is assembled from local bicontact geometry. The Anosov condition looks global (every orbit must be hyperbolic), but the bicontact plug construction makes it local: if each piece is bicontact and the pieces glue correctly, the flow is Anosov. Local geometry, plus compatible gluing, produces global dynamics.
2603.22250. Dynamical systems / Anosov flows / bicontact structures / hyperbolic plugs / 3-manifolds.