Israel Journal of Mathematics

, Volume 31, Issue 3, pp 298–314

Bernoulliflows over maps of the interval

  • M. Ratner

DOI: 10.1007/BF02761496

Cite this article as:
Ratner, M. Israel J. Math. (1978) 31: 298. doi:10.1007/BF02761496


We consider special flowsT′ built over shift automorphismϕ with a Holder function. We introduce two properties forϕ (R and WM) s.t. weak-mixing forT′ impliesK ifϕ is R and it implies Bernoulliness ifϕ is WM. We apply this to maps of the interval to show that for the Lorentz Attractor Flow with a natural measure weak-mixing implies Bernoulliness.

Copyright information

© The Weizmann Science Press of Israel 1978

Authors and Affiliations

  • M. Ratner
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA