Explores the U(1)-extension of Anosov diffeomorphisms and the proof of exponential mixing through uniform contractivity and cancellation by complex phases.
Explores infinitesimal deformations of one-dimensional maps, discussing common characteristics, methods, and recent results in expanding and piecewise expanding maps.
Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.
Covers the properties of the exponential map in Lie groups and their algebras, including smoothness and the relationship between subgroups and algebras.