2019/07/18 by An Chen, Chen, An, Xueting Tian +1
Computer Science · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.1907.09400
openalex publication_date 2019/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It follows from Oseledec Multiplicative Ergodic Theorem (or Kingmans Subadditional Ergodic Theorem) that the Lyapunov-irregular set of points for which the Oseledec averages of a given continuous cocycle diverge has zero measure with respect to any invariant probability measure. In strong contrast, for any dynamical system f with exponential specification property and a Holder continuous matrix cocycle A, we show here that if there exist ergodic measures with different Lyapunov spectrum, then the Lyapunov-irregular set of A displays distributional chaos of type 1.