caa a22 4500 469068361 CHVBK 20180323132914.0 cr unu---uuuuu 170328e19920201xx s 000 0 eng 10.1007/BF02764801 doi (NATIONALLICENCE)springer-10.1007/BF02764801 Finitarily deterministic generators for zero entropy systems [Elektronische Daten] [Steven Kalikow, Yitzhak Katznelson, Benjamin Weiss] Zero entropy processes are known to be deterministic—the past determines the present. We show that each is isomorphic, as a system, to a finitarily deterministic one, i.e., one in which to determine the present from the past it suffices to scan a finite (of random length) portion of the past. In fact we show more: the finitary scanning can be done even if the scanner is noisy and passes only a small fraction of the readings, provided the noise is independent of our system. The main application we present here is that any zero entropy system can be extended to a random Markov process (namely one in which the conditional distribution of the present given the past is a mixture of finite state Markov chains). This allows one to study zero entropy transformations using a procedure completely different from the usual cutting and stacking. The Magnes Press, 1992 Kalikow Steven Department of Mathematics, Cornell University, Ithaca, N.Y., U.S.A. aut Katznelson Yitzhak Department of Mathematics, Stanford University, 94305-2125, Stanford, CD, U.S.A. aut Weiss Benjamin Department of Mathematics, Hebrew University, Jerusalem, Israel aut Israel Journal of Mathematics Springer-Verlag 79/1(1992-02-01), 33-45 0021-2172 79:1<33 1992 79 11856 https://doi.org/10.1007/BF02764801 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02764801 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kalikow Steven Department of Mathematics, Cornell University, Ithaca, N.Y., U.S.A aut NATIONALLICENCE 700 1- Katznelson Yitzhak Department of Mathematics, Stanford University, 94305-2125, Stanford, CD, U.S.A aut NATIONALLICENCE 700 1- Weiss Benjamin Department of Mathematics, Hebrew University, Jerusalem, Israel aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer-Verlag 79/1(1992-02-01), 33-45 0021-2172 79:1<33 1992 79 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer