Rigid measures on the torus. - Brown, Aaron. (2017)
Abstract: Given a measure &mu on a manifold M , we wish to characterize all smooth dynamics preserving &mu. We consider measures &mu supported on the two-torus and study the group of &mu-preserving diffeomorphisms. For &mu invariant under an Anosov diffeomorphism, we find conditions for which the group of &mu-preserving diffeomorphisms is `essentially' cyclic.; Thesis (Ph.D.)--Tufts University, 2011.; Submitted to the Dept. of Mathematics.; Advisor: Boris Hasselblatt.; Committee: Genevieve Walsh, Zbigniew Nitecki, and Keith Burns.; Keyword: Mathematics.