Markov structures and decay of correlations for non-uniformly expanding dynamical systems
Metastability in the Furstenberg-Zimmer tower
According to the Furstenberg-Zimmer structure theorem, every measure-preserving system has a maximal distal factor, and is weak mixing relative to that factor. Furstenberg and Katznelson used this structural analysis of measure-preserving systems to provide a perspicuous proof of Szemerédi’s theorem. Beleznay and Foreman showed that, in general, the transfinite construction of the maximal distal factor of a separable measure-preserving system can extend arbitrarily far into the countable ordinals....
Mischungseigenschaften und Entropie beim Jacobischen Algorithmus.
Mixing actions of groups with the Haagerup approximation property
A countable group Γ has the Haagerup approximation property if and only if the mixing actions are dense in the space of all actions of Γ.
Mixing automorphisms of compact groups and a theorem of Schlickewei.
Mixing on rank-one transformations
We prove that mixing on rank-one transformations is equivalent to "the uniform convergence of ergodic averages (as in the mean ergodic theorem) over subsequences of partial sums". In particular, all polynomial staircase transformations are mixing.
Mixing properties of nearly maximal entropy measures for shifts of finite type
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.
Mixing rank-one actions of locally compact abelian groups
Mixing via families for measure preserving transformations
In topological dynamics a theory of recurrence properties via (Furstenberg) families was established in the recent years. In the current paper we aim to establish a corresponding theory of ergodicity via families in measurable dynamical systems (MDS). For a family ℱ (of subsets of ℤ₊) and a MDS (X,,μ,T), several notions of ergodicity related to ℱ are introduced, and characterized via the weak topology in the induced Hilbert space L²(μ). T is ℱ-convergence ergodic of order k if for any of positive...
Multiple return times theorems for weakly mixing systems