Ergodic behavior of graph entropy.
Kieffer, John, Yang, En-hui (1997)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Kieffer, John, Yang, En-hui (1997)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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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...
S. Janković (1989)
Matematički Vesnik
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Bobok, J. (2003)
Acta Mathematica Universitatis Comenianae. New Series
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Karel Winkelbauer (1970)
Kybernetika
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Christian Grillenberger (1980)
Mathematische Zeitschrift
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J.-P. Thouvenot (2009)
Fundamenta Mathematicae
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We describe the natural framework in which the relative spectral theory is developed. We give some results and indicate how they relate to two open problems in ergodic theory. We also compute the relative entropy of gaussian extensions of ergodic transformations.
David Burguet (2010)
Colloquium Mathematicae
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A nonuniformly entropy expanding map is any ¹ map defined on a compact manifold whose ergodic measures with positive entropy have only nonnegative Lyapunov exponents. We prove that a nonuniformly entropy expanding map T with r > 1 has a symbolic extension and we give an explicit upper bound of the symbolic extension entropy in terms of the positive Lyapunov exponents by following the approach of T. Downarowicz and A. Maass [Invent. Math. 176 (2009)].
Nikita Sidorov, Anatoly Vershik (1998)
Monatshefte für Mathematik
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Eli Glasner, Benjamin Weiss (1994)
Bulletin de la Société Mathématique de France
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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.
Young-Ho Ahn, Dou Dou, Kyewon Koh Park (2010)
Studia Mathematica
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Recently the notions of entropy dimension for topological and measurable dynamical systems were introduced in order to study the complexity of zero entropy systems. We exhibit a class of strictly ergodic models whose topological entropy dimensions range from zero to one and whose measure-theoretic entropy dimensions are identically zero. Hence entropy dimension does not obey the variational principle.
Fumio Hiai, Dénes Petz (2007)
Banach Center Publications
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A new expression as a certain asymptotic limit via "discrete micro-states" of permutations is provided for the mutual information of both continuous and discrete random variables.