4 citations · 4 across the 7 of their papers we have counts for
10 papers
Lyapunov spectrum of homoclinic classes
Lorenzo J. Díaz, Katrin Gelfert, Xiaodong Wang +1
We study the Lyapunov spectrum of the ergodic measures of isolated homoclinic classes of -generic diffeomorphisms. We show that this spectrum has nonempty interior and that an…
Denseness of zero entropy aperiodic ergodic measures
Camila Crispin, Lorenzo J. Díaz
We study partially hyperbolic homoclinic classes of -generic diffeomorphisms with a one-dimensional central bundle, so that the central Lyapunov exponent is well defi…
Robust heterodimensional cycles of co-index two via split blending machines
Pablo G. Barrientos, Lorenzo J. Díaz, Yuri Ki +2
We consider diffeomorphisms with heterodimensional cycles of co-index two, associated with saddles and having unstable indices and , respectively. In a p…
Full flexibility of entropies among ergodic measures for partially hyperbolic diffeomorphisms
Lorenzo J. Díaz, Katrin Gelfert, Michal Rams +1
We study nonhyperbolic and transitive partially hyperbolic diffeomorphisms having a one-dimensional center. We prove joint flexibility with respect to entropy and center Lyapunov e…
A Conservative Partially Hyperbolic Dichotomy: Hyperbolicity versus Nonhyperbolic Measures
Lorenzo J. Díaz, Jiagang Yang, Jinhua Zhang
In a conservative and partially hyperbolic three-dimensional setting, we study three representative classes of diffeomorphisms: those homotopic to Anosov (or Derived from Anosov di…
The amount of nonhyperbolicity for partially hyperbolic diffeomorphisms
Lorenzo J. Díaz, Katrin Gelfert, Jinhua Zhang
We study the amount of nonhyperbolicity within a broad class of (nonhyperbolic) partially hyperbolic diffeomorphisms with a one-dimensional center. For that, we focus on the center…
Loosely Bernoulli zero exponent measures for elliptic matrix cocycles
L. J. Díaz, K. Gelfert, M. Rams
For an open and dense subset of elliptic matrix cocycles, we construct a family of loosely Bernoulli ergodic measures with zero top Lyapunov exponent. This…
Variational principle for nonhyperbolic ergodic measures: Skew products and elliptic cocycles
Lorenzo J. Díaz, Katrin Gelfert, Michał Rams
For a large class of transitive non-hyperbolic systems, we construct nonhyperbolic ergodic measures with entropy arbitrarily close to its maximal possible value. The systems we con…
The structure of the space of ergodic measures of transitive partially hyperbolic sets
Lorenzo J. Díaz, Katrin Gelfert, Tiane Marcarini +1
We provide examples of transitive partially hyperbolic dynamics (specific but paradigmatic examples of homoclinic classes) which blend different types of hyperbolicity in the one-d…
Entropy spectrum of Lyapunov exponents for nonhyperbolic step skew-products and elliptic cocycles
Lorenzo J. Díaz, Katrin Gelfert, Michał Rams
We study the fiber Lyapunov exponents of step skew-product maps over a complete shift of , , symbols and with diffeomorphisms of the circle as fiber maps. The syste…