2023/11/15 by Lorenzo J. Díaz, Katrin Gelfert, Díaz, L. J. +3
Computer Science · Mathematics · Physics and Astronomy · #15B99 #37A35 #37D25 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2311.09351
openalex publication_date 2023/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
For an open and dense subset of elliptic \rm SL(2,\mathbb R) matrix cocycles, we construct a family of loosely Bernoulli ergodic measures with zero top Lyapunov exponent. This provides a counterpart to a classical result by Furstenberg. The construction gives also an f-connected set of measures with these properties whose entropies vary continuously from zero to almost the maximal possible value. We also obtain an analogous result for an open class of nonhyperbolic step skew products with \mathbb S1 diffeomorphism fiber maps. Our approach combines substitution schemes between finite letter alphabets and differentiable dynamics.