Universally finitary symbolic extensions
We prove that by considering a finitary (almost continuous) symbolic extension of a topological dynamical system instead of a continuous extension, one cannot achieve any drop of the entropy of the extension.
On the countable generator theorem
Let T be a finite entropy, aperiodic automorphism of a nonatomic probability space. We give an elementary proof of the existence of a finite entropy, countable generating partition for T.
Phenomena in rank-one ℤ²-actions
We present an example of a rank-one partially mixing ℤ²-action which possesses a non-rigid factor and for which the Weak Closure Theorem fails. This is in sharp contrast to one-dimensional actions, which cannot display this type of behavior.
Fiber entropy and conditional variational principles in compact non-metrizable spaces
We consider a pair of topological dynamical systems on compact Hausdorff (not necessarily metrizable) spaces, one being a factor of the other. Measure-theoretic and topological notions of fiber entropy and conditional entropy are defined and studied. Abramov and Rokhlin's definition of fiber entropy is extended, using disintegration. We prove three variational principles of conditional nature, partly generalizing some results known before in metric spaces: (1) the topological conditional entropy...
Residuality of dynamical morphisms
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.
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