Strictly ergodic patterns and entropy for interval maps.
Bobok, J. (2003)
Acta Mathematica Universitatis Comenianae. New Series
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Bobok, J. (2003)
Acta Mathematica Universitatis Comenianae. New Series
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Jon Aaronson, Kyewon Koh Park (2009)
Fundamenta Mathematicae
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We show that a certain type of quasifinite, conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic, measure preserving transformation which is not quasifinite; and consider distribution asymptotics of information showing that e.g. for Boole's transformation, information is asymptotically mod-normal with normalization ∝ √n. Lastly, we show that certain ergodic, probability...
Magda Komorníková, Jozef Komorník (1983)
Mathematica Slovaca
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Magda Komorníková, Jozef Komorník (1982)
Mathematica Slovaca
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Eli Glasner, Benjamin Weiss (1994)
Bulletin de la Société Mathématique de France
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Nikita Sidorov, Anatoly Vershik (1998)
Monatshefte für Mathematik
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Tomasz Downarowicz, Dawid Huczek (2012)
Studia Mathematica
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We prove that every topological dynamical system (X,T) has a faithful zero-dimensional principal extension, i.e. a zero-dimensional extension (Y,S) such that for every S-invariant measure ν on Y the conditional entropy h(ν | X) is zero, and, in addition, every invariant measure on X has exactly one preimage on Y. This is a strengthening of the authors' result in Acta Appl. Math. [to appear] (where the extension was principal, but not necessarily faithful).
R. Burton, M. Keane, Jacek Serafin (2000)
Colloquium Mathematicae
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We present a unified approach to the finite generator theorem of Krieger, the homomorphism theorem of Sinai and the isomorphism theorem of Ornstein. We show that in a suitable space of measures those measures which define isomorphisms or respectively homomorphisms form residual subsets.