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1
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Universally finitary symbolic extensions

100%
Serafin J.
Fundamenta Mathematicae
|
2009
|
tom 206
|
nr 1
281-285
EN
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.
2
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Phenomena in rank-one ℤ²-actions

64%
Downarowicz T., Serafin J.
Studia Mathematica
|
2009
|
tom 192
|
nr 3
281-294
EN
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.
3
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Most monothetic extensions are rank-1

64%
Iwanik A., Serafin J.
Colloquium Mathematicum
|
1993
|
tom 66
|
nr 1
63-76
4
Content available remote

On the countable generator theorem

64%
Keane M. S., Serafin J.
Fundamenta Mathematicae
|
1998
|
tom 157
|
nr 2-3
255-259
EN
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.
5
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Fiber entropy and conditional variational principles in compact non-metrizable spaces

64%
Downarowicz T., Serafin J.
Fundamenta Mathematicae
|
2002
|
tom 172
|
nr 3
217-247
EN
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 equals the supremum of the topological fiber entropy over the factor, which also equals the supremum of the topological fiber entropy given a measure over all invariant measures on the factor, (2) the topological fiber entropy given a measure equals the supremum of the measure-theoretic conditional entropy over all invariant measures on the larger system projecting to the given one. Combining the above, we get (3) the topological conditional entropy equals the supremum of the measure-theoretic conditional entropy over all invariant measures. A tail entropy of a measure is introduced in totally disconnected spaces. As an application of our variational principles it is proved that the tail entropy estimates from below the "defect of upper semicontinuity" of the entropy function.
6
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Residuality of dynamical morphisms

51%
Burton R. M., Keane M. S., Serafin J.
Colloquium Mathematicum
|
2000
|
tom 84/85
|
nr 2
307-317
EN
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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