Singular Baker’s maps and Lorenz’s Pretzels
Isabel Rios (UFF)

We present a family of non-uniformly hyperbolic transformations, which we call singular baker’s maps, or SBM, on the unit square. The SBMs are, on a residual full-measure (for "almost all" ergodic measures) subset of the space, topologically conjugated to a shift of bilateral sequences on two symbols. From this conjugacy we get transitivity and density of hyperbolic periodic points for the SBM. We then describe a singular differentiable semi-flow in dimension 3 having a transitive compact invariant set with nonempty interior, in which closed hyperbolic orbits are dense and accumulate in a hyperbolic singularity. We call this set a Lorenz’s pretzel. It is a joint work with Romulo Rosa.