On some common misconceptions regarding the "Ergodic Hierarchy"

Details On some common misconceptions regarding the "Ergodic Hierarchy" On some common misconceptions regarding the "Ergodic Hierarchy"

2004-07-28

arxiv.org/abs/cond-mat/0407730v1

Physics

Condensed Matter

Statistical Mechanics

2 pages

Scientific paper

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.

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