Invariant measures on stationary Bratteli diagrams

By S. Bezuglyi, J. Kwiatkowski, Konstantin Medynets, Boris Solomyak. Ergodic Theory and Dynamical Systems, 2008

85 citations recorded by the source corpus.

Abstract We study dynamical systems acting on the path space of a stationary (non-simple) Bratteli diagram. For such systems we give an explicit description of all ergodic probability measures that are invariant with respect to the tail equivalence relation (or the Vershik map); these measures are completely described by the incidence matrix of the Bratteli diagram. Since such diagrams correspond to substitution dynamical systems, our description provides an algorithm for finding invariant probability measures for aperiodic non-minimal substitution systems. Several corollaries of these results are obtained. In particular, we show that the invariant measures are not mixing and give a criterion for a complex number to be an eigenvalue for the Vershik map.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e004b3cbc6e3aa86b80daae3bfce21b6158d8507

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. S. Bezuglyi
2. J. Kwiatkowski
3. Boris Solomyak
4. Konstantin Medynets
5. Pablo Shmerkin

In Mathematical Physics

1. S. Bezuglyi
2. J. Kwiatkowski
3. Boris Solomyak
4. Konstantin Medynets
5. Pablo Shmerkin
6. Jonathan M. Fraser

Citations in the corpus

• Finite rank Bratteli diagrams: Structure of invariant measures (2010, methodology): “This result generalizes the corresponding facts on linearly recurrent systems [CDHM03] and substitution systems [DK78], [BKMS10].”