Resumen de Non-periodic bifurcations of one-dimensional maps

Vanderlei Horita, Nivaldo Muniz, Paulo Rogério Sabini

• We prove that a ¿positive probability¿ subset of the boundary of ¿{uniformly expanding circle transformations}¿ consists of Kupka¿Smale maps. More precisely, we construct an open class of two-parameter families of circle maps $(f_{a,\theta})_{a,\theta}$ such that, for a positive Lebesgue measure subset of values of $a$, the family $(f_{a,\theta})_\theta$ crosses the boundary of the uniformly expanding domain at a map for which all periodic points are hyperbolic (expanding) and no critical point is pre-periodic. Furthermore, these maps admit an absolutely continuous invariant measure. We also provide information about the geometry of the boundary of the set of hyperbolic maps.