5 papers
Robust existence of nonhyperbolic ergodic measures with positive entropy and full support
Christian Bonatti, Lorenzo J. Díaz, Dominik Kwietniak
We prove that for some manifolds the set of robustly transitive partially hyperbolic diffeomorphisms of with one-dimensional nonhyperbolic centre direction contains a …
Non-hyperbolic Iterated Function Systems: semifractals and the chaos game
Lorenzo J. Díaz, Edgar Matias
We consider iterated functions systems (IFS) on compact metric spaces and introduce the concept of target sets. Such sets have very rich dynamical properties and play a similar rol…
Blender-horseshoes in center-unstable Hénon-like families
Lorenzo J. Díaz, Sebastián A. Pérez
A blender-horseshoe is a locally maximal transitive hyperbolic set that appears in dimension at least three carrying a distinctive geometrical property: its local stable manifold "…
Hyperbolic graphs: critical regularity and box dimension
Lorenzo J. Díaz, Katrin Gelfert, Maik Gröger +1
We study fractal properties of invariant graphs of hyperbolic and partially hyperbolic skew product diffeomorphisms in dimension three. We describe the critical (either Lipschitz o…
Non-hyperbolic Iterated Function Systems: attractors and stationary measures
Edgar Matias, Lorenzo J. Díaz
We consider iterated function systems consisting of continuous self maps of a compact metric space . We introduce the subset of {\…