Cantor aperiodic systems and Bratteli diagrams

By Konstantin Medynets. 2006

71 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/605e7fe8d70b672b7d2101ca32095b6e4843ab43

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. Kate Juschenko
6. Mikael de la Salle
7. Volodymyr V. Nekrashevych
8. Val'erie Berth'e

In Geometry and Topology

1. Volodymyr V. Nekrashevych
2. S. Bezuglyi
3. J. Kwiatkowski
4. Kate Juschenko
5. Mikael de la Salle
6. Boris Solomyak
7. Val'erie Berth'e
8. Jörg M. Thuswaldner

In Mathematical Physics

1. Volodymyr V. Nekrashevych
2. S. Bezuglyi
3. J. Kwiatkowski
4. Mikael de la Salle
5. Boris Solomyak
6. Kate Juschenko
7. Val'erie Berth'e
8. Jörg M. Thuswaldner

Citations in the corpus

• Aperiodic substitution systems and their Bratteli diagrams (2007, methodology): “Bratteli diagrams in this case [BDM], [ Med ].”
• Invariant measures on stationary Bratteli diagrams (2008, methodology): “It is shown in [Med] that there are stationary Bratteli diagrams which do not admit a Vershik map.”
• Extensions of amenable groups by recurrent groupoids (2013, methodology): “ery minimal homeomorphism of the Cantor set (i.e., a homeomorphism for which every orbit is dense) is topologically conjugate to the adic transformation defined by a Bratteli-Vershik diagram. See also [Med06] where Vershik-Bratteli diagrams are used to describe aperiodic homeomorphisms, i.e., homeomo”
• Recognizability for sequences of morphisms (2017, background): “eoretic BratteliVershik representations always exist for ergodic systems [Ver85], as do topological Bratteli-Vershik representations for (not necessarily primitive) aperiodic Cantor dynamical systems [Med06]. The question is when a naturally constructed representation exists. For example, the repres”
• FULL GROUPS, FLIP CONJUGACY, AND ORBIT EQUIVALENCE OF CANTOR MINIMAL SYSTEMS (2006, methodology): “Using the arguments of [BDM, Proposition 3] (see also [ M2 , Lemma 2.2]), we can show that there exists a clopen set B ⊂ X≥k such that gi(B) ∩B = ∅ for i = 0,...,k −1 and”
• Finite rank Bratteli diagrams: Structure of invariant measures (2010, background): “cussed in numerous recent papers, they might be considered as almost classical nowadays, so we avoid giving detailed definitions. An interested reader may consult the papers [HPS92], [GPS95], [DHS99], [Me06], [BKM09], [BKMS10], and references therein for all details concerning Bratteli diagrams and V”