2004/07/28 by Henk van Beijeren, van Beijeren, Henk
Engineering · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Dynamics and Fractals #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0407730
2 pages
arxiv created 2004/07/28 · openalex publication_date 2004/07/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The well-known ergodic hierarchy of sheerly ergodic, mixing, Kolmogorov and Bernoulli systems, with each next level supposedly encompassing the previous one, is shown to be too simplistic in its usual formulation. A K-system can be sheerly ergodic and sometimes may be reduced to a sheerly mixing system by some simple projection. More precise characterizations of ergodic properties of dynamical systems should start out from a consideration of the full Lyapunov spectrum.