Displaying similar documents to “Predictability, entropy and information of infinite transformations”

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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Symbolic extensions for nonuniformly entropy expanding maps

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 r 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)].

Zero Krengel entropy does not kill Poisson entropy

Élise Janvresse, Thierry de la Rue (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We prove that the notions of Krengel entropy and Poisson entropy for infinite-measure-preserving transformations do not always coincide: We construct a conservative infinite-measure-preserving transformation with zero Krengel entropy (the induced transformation on a set of measure 1 is the Von Neumann–Kakutani odometer), but whose associated Poisson suspension has positive entropy.

Relative spectral theory and measure-theoretic entropy of gaussian extensions

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.

Entropy dimension and variational principle

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.

Residuality of dynamical morphisms

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.