By Jon Aaronson (auth.), Manfred Denker, Konrad Jacobs (eds.)
ISBN-10: 3540095179
ISBN-13: 9783540095170
ISBN-10: 3540351302
ISBN-13: 9783540351306
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Additional resources for Ergodic Theory: Proceedings, Oberwolfach, Germany, June 11–17, 1978
Example text
Boundary matrJ× function ~ ) of when with 0 . Let ~tn domain which are the IIA[I d e p o t e ~s ~i~,en D, let the 3g Definition. fD(s,8) Definition. tion, i If B) + ilh' - Ill ]. is a n n - f l o w and P = {P : i 6 ~ a finite parti1 a function PD(X) : D ~ [ . PD(X) (v) is t h a t N P C v x 6 Pi " _ o w d e f i n e dD(X,y) = dD(PD(x)'PD(Y))" then we define for w h i c h P fD(x,y) Similarly, There tion P it d o e s for w h i c h finition of LB to f l o w s of tion zero for and even e > 0 (¢,P) LK if trization.
I ( A j ( ~ (A) and aperiodic. 1) for some Then the set Tower Theorem and Halmos' be a measurable d(Qi) we may prove satisfying d(f-lg Proof: B, Thus, Theorem 1 and the Conjugacy Lemma as Rohlin's and matrices i' for all Repeated A in F. 24 Consequently ~N(A) .. • , n} = {i, for all A in ~ B N > 0, and or , B is aperiodic. , n, Let f g f(x) E Pj h(x) and be any transformation [ 8, p. 74]). , n x E Qi" h Qi ~ Qj # of Then almost ~' and surely f-lg f(x) f(x) E Qj. ~. (see E Pi and Also, E h(Qi) , so d(f -I g f(x), h(x)) !
On flows, three Y are (X,~) let and ~ and respectively, disjoint. conditions: is an e q u i v a l e n c e Then and Suppose (i) p o i n t dis- relation (Y,9) are topologically disjoint. That The unique sufficiency ergodicity of the on t r a n s f o r m a t i o n stating this formation x@ x with and such (X,T) a dense orbit relation z xt n in extension and X. proximal, if, that If and Y non-empty open are m e t r i c are m i n i m a l set ric ~') if t h e r e is o b t a i n e d general That is, highly flow from proximal there The t r a n s - point).
Ergodic Theory: Proceedings, Oberwolfach, Germany, June 11–17, 1978 by Jon Aaronson (auth.), Manfred Denker, Konrad Jacobs (eds.)
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