Partially hyperbolic dieomorphisms acting quasi-isometric on the center
Santiago Martinchich (UDELAR, Uruguai)

A key tool in the study of partially hyperbolic dieomorphisms is the presence of invariant foliations. Given an invariant foliation tangent to the center bundle, we say that the dieomorphism acts quasiisometrically on it if there exist two constants r>0 and R>0 such that any pair of points at center distance less than r stay at distance less than R for every positive and negative iterate. I will present the following classication result for 3-dimensional transitive partially hyperbolic dieomorphisms acting quasi-isometrically on the center: modulo nite lift and iterates, the system is a skew-product (the center foliation is uniformly compact) or is a discretized Anosov ows. Work in progress with Marcielis Espitia and Rafael Potrie.