Markovian Families in the Bifoliated Plane of Anosov Flows in Dimension 3

Explore a 31-minute lecture on Markovian families in the bifoliated plane of Anosov flows in three dimensions. Delve into a novel approach for classifying transitive Anosov flows on 3-manifolds up to orbital equivalence. Learn about the generalization of Markov partitions and the introduction of Markovian families in the bifoliated plane. Discover how these families are associated with two key combinatorial invariants: one describing the flow up to Dehn-Goodman-Fried surgeries on specific periodic orbits, and another describing it up to orbital equivalence. Engage with open questions surrounding these combinatorial invariants and their potential role in classifying Anosov flows in three dimensions. Gain insights into advanced topics in dynamical systems and differential geometry through this talk presented at the Simons Semester on Dynamics.

Ioannis Iakovoglou