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Displaying similar documents to “Mertens theorem and closed orbits of ergodic toral automorphisms.”

Automorphisms with exotic orbit growth

Stephan Baier, Sawian Jaidee, Shaun Stevens, Thomas Ward (2013)

Acta Arithmetica

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The dynamical Mertens' theorem describes asymptotics for the growth in the number of closed orbits in a dynamical system. We construct families of ergodic automorphisms of fixed entropy on compact connected groups with a continuum of growth rates on two different growth scales. This shows in particular that the space of all ergodic algebraic dynamical systems modulo the equivalence of shared orbit-growth asymptotics is not countable. In contrast, for the equivalence relation of measurable...

Ergodic automorphisms whose weak closure of off-diagonal measures consists of ergodic self-joinings

Y. Derriennic, K. Frączek, M. Lemańczyk, F. Parreau (2008)

Colloquium Mathematicae

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Basic ergodic properties of the ELF class of automorphisms, i.e. of the class of ergodic automorphisms whose weak closure of measures supported on the graphs of iterates of T consists of ergodic self-joinings are investigated. Disjointness of the ELF class with: 2-fold simple automorphisms, interval exchange transformations given by a special type permutations and time-one maps of measurable flows is discussed. All ergodic Poisson suspension automorphisms as well as dynamical systems...

On subrelations of ergodic measured type III equivalence relations

Alexandre Danilenko (2000)

Colloquium Mathematicae

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We discuss the classification up to orbit equivalence of inclusions 𝑆 ⊂ ℛ of measured ergodic discrete hyperfinite equivalence relations. In the case of type III relations, the orbit equivalence classes of such inclusions of finite index are completely classified in terms of triplets consisting of a transitive permutation group G on a finite set (whose cardinality is the index of 𝑆 ⊂ ℛ), an ergodic nonsingular ℝ-flow V and a homomorphism of G to the centralizer of V.

Finitary orbit equivalence and measured Bratteli diagrams

T. Hamachi, M. S. Keane, M. K. Roychowdhury (2008)

Colloquium Mathematicae

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We prove a strengthened version of Dye's theorem on orbit equivalence, showing that if the transformation structures are represented as finite coordinate change equivalence relations of ergodic measured Bratteli diagrams, then there is a finitary orbit equivalence between these diagrams.