B. Kamiński, K. Park (1999)
Studia Mathematica
Similarity:
We define the concept of directional entropy for arbitrary -actions on a Lebesgue space, we examine its basic properties and consider its behaviour in the class of product actions and rigid actions.
Avni, Nir (2005)
Electronic Research Announcements of the American Mathematical Society [electronic only]
Similarity:
Valentin Golodets, Sergey Sinel'shchikov (2000)
Colloquium Mathematicae
Similarity:
The existence of non-Bernoullian actions with completely positive entropy is proved for a class of countable amenable groups which includes, in particular, a class of Abelian groups and groups with non-trivial finite subgroups. For this purpose, we apply a reverse version of the Rudolph-Weiss theorem.
Anatole Katok, Jean-Paul Thouvenot (1997)
Annales de l'I.H.P. Probabilités et statistiques
Similarity:
Matthew Foreman, Benjamin Weiss (2004)
Journal of the European Mathematical Society
Similarity:
Despite many notable advances the general problem of classifying ergodic measure preserving transformations (MPT) has remained wide open. We show that the action of the whole group of MPT’s on ergodic actions by conjugation is turbulent in the sense of G. Hjorth. The type of classifications ruled out by this property include countable algebraic objects such as those that occur in the Halmos–von Neumann theorem classifying ergodic MPT’s with pure point spectrum. We treat both the classical...
David Burguet (2010)
Colloquium Mathematicae
Similarity:
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)].
E. Robinson, Ayşe Şahin (2000)
Colloquium Mathematicae
Similarity:
We prove that for a certain class of shifts of finite type with positive topological entropy there is always an invariant measure, with entropy arbitrarily close to the topological entropy, that has strong metric mixing properties. With the additional assumption that there are dense periodic orbits, one can ensure that this measure is Bernoulli.
J.-P. Thouvenot (2009)
Fundamenta Mathematicae
Similarity:
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.
Alvaro Coronel, Alejandro Maass, Song Shao (2009)
Studia Mathematica
Similarity:
We study relationships between sequence entropy and the Kronecker and rigid algebras. Let (Y,,ν,T) be a factor of a measure-theoretical dynamical system (X,,μ,T) and S be a sequence of positive integers with positive upper density. We prove there exists a subsequence A ⊆ S such that for all finite partitions ξ, where (X|Y) is the Kronecker algebra over . A similar result holds for rigid algebras over . As an application, we characterize compact, rigid and mixing extensions via relative...
S. Thangavelu (1991)
Studia Mathematica
Similarity:
B. Kamiński (1990)
Studia Mathematica
Similarity:
Mariusz Lemańczyk (1985)
Studia Mathematica
Similarity:
R. Burton, M. Keane, Jacek Serafin (2000)
Colloquium Mathematicae
Similarity:
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.