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Abstract: These diffeomorphisms exhibit weaker forms of hyperbolicity and are extremely common. We study these in dimension 3 and prove some rigidity or classification results. We assume that the diffeomorphism is homotopic to the identity, and show that certain invariant foliations associated with the diffeomorphism have a structure that is well determined. This has some important consequences when the manifold is either hyperbolic or Seifert: under certain conditions we prove the diffeomorphism is up to iterates and finite covers, leaf conjugate to the time map of a topological Anosov flow.

This is joint work with Thomas Barthelme, Steven Frankel, and Rafael Potrie.