English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We analyse certain Haar systems associated to groupoids obtained by certainnatural equivalence relations of dynamical nature on sets like$\{1,2,...,d\}^\mathbb{Z}$, $\{1,2,...,d\}^\mathbb{N}$, $S^1\times S^1$, or$(S^1)^\mathbb{N}$, where $S^1$ is the unitary circle. We also describeproperties of transverse functions, quasi-invariant probabilities and KMSstates for some examples of von Neumann algebras (and also $C^*$-Algebras)associated to these groupoids. We relate some of these KMS states with Gibbsstates of Thermodynamic Formalism. While presenting new results, we will alsodescribe in detail several examples and basic results on the above topics. Inother words it is also a survey paper. Some known results on non-commutativeintegration are presented, more precisely, the relation of transverse measures,cocycles and quasi-invariant probabilities.  We describe the results in a language which is more familiar to people inDynamical Systems. Our intention is to study Haar systems, quasi-invariantprobabilities and von Neumann algebras as a topic on measure theory(intersected with ergodic theory) avoiding questions of algebraic nature(which, of course, are also extremely important).

Haar systems, KMS states on von Neumann algebras and $C^*$-algebras on dynamically defined groupoids and Noncommutative Integration