26 citations · 51 across the 9 of their papers we have counts for
10 papers
Homoclinic tangencies leading to robust heterodimensional cycles
Pablo G. Barrientos, Lorenzo J. Díaz, Sebastián A. Pérez
We consider () diffeomorphisms defined on manifolds of dimension with homoclinic tangencies associated to saddles. Under generic properties, w…
Mingled hyperbolicities: ergodic properties and bifurcation phenomena (an approach using concavity)
L. J. Díaz, K. Gelfert, M. Rams
We consider skew-products with concave interval fiber maps over a certain subshift obtained as the projection of orbits staying in a given region. It generates a new type of (essen…
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 "…
Stability of the Markov operator and synchronization of Markovian random products
Lorenzo J. Díaz, Edgar Matias
We study Markovian random products on a large class of "m-dimensional" connected compact metric spaces (including products of closed intervals and trees). We introduce a splitting…
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 {\…
Blenders in center unstable Hénon-like families: with an application to heterodimensional bifurcations
Lorenzo J. Díaz, Shin Kiriki, Katsutoshi Shinohara
We give an explicit family of polynomial maps called center unstable Hénon-like maps and prove that they exhibits blenders for some parametervalues. Using this family, we also prov…
Rich phase transitions in step skew-products
Lorenzo J. Díaz, Katrin Gelfert, Michał Rams
We present examples of partially hyperbolic and topologically transitive local diffeomorphisms defined as skew products over a horseshoe which exhibit rich phase transitions for th…