scholarly journals Random orderings and unique ergodicity of automorphism groups

2014 ◽  
Vol 16 (10) ◽  
pp. 2059-2095 ◽  
Author(s):  
Omer Angel ◽  
Alexander Kechris ◽  
Russell Lyons
Keyword(s):  
Automorphism Groups ◽  
Unique Ergodicity

scholarly journals Amenability and unique ergodicity of automorphism groups of countable homogeneous directed graphs

2018 ◽  
Vol 40 (5) ◽  
pp. 1351-1401
Author(s):  
MICHEAL PAWLIUK ◽  
MIODRAG SOKIĆ
Keyword(s):  
Automorphism Groups ◽  
Directed Graphs ◽  
Point Of View ◽  
Unique Ergodicity ◽  
Minimal Flow ◽  
Negative Results ◽  
Starting Point ◽  
Complete Multipartite ◽  
Uniquely Ergodic

We study the automorphism groups of countable homogeneous directed graphs (and some additional homogeneous structures) from the point of view of topological dynamics. We determine precisely which of these automorphism groups are amenable (in their natural topologies). For those which are amenable, we determine whether they are uniquely ergodic, leaving unsettled precisely one case (the ‘semi-generic’ complete multipartite directed graph). We also consider the Hrushovski property. For most of our results we use the various techniques of Angelet al[Random orderings and unique ergodicity of automorphism groups.J. Eur. Math. Soc.,16(2014), 2059–2095], suitably generalized to a context in which the universal minimal flow is not necessarily the space of all orders. Negative results concerning amenability rely on constructions of the type considered in Zucker [Amenability and unique ergodicity of automorphism groups of Fraïssé structures.Fund. Math.,226(2014), 41–61]. An additional class of structures (compositions) may be handled directly on the basis of very general principles. The starting point in all cases is the determination of the universal minimal flow for the automorphism group, which in the context of countable homogeneous directed graphs is given in Jasińskiet al[Ramsey precompact expansions of homogeneous directed graphs.Electron. J. Combin.,21(4), (2014), 31] and the papers cited therein.

Teichmüller dynamics and unique ergodicity via currents and Hodge theory

2020 ◽  
Vol 2020 (768) ◽  
pp. 39-54
Author(s):  
Curtis T. McMullen
Keyword(s):  
Hodge Theory ◽  
Unique Ergodicity ◽  
Polygonal Billiards ◽  
Teichmuller Dynamics

AbstractWe present a cohomological proof that recurrence of suitable Teichmüller geodesics implies unique ergodicity of their terminal foliations. This approach also yields concrete estimates for periodic foliations and new results for polygonal billiards.

Pentavalent 1-Transitive Digraphs with Non-Solvable Automorphism Groups

2020 ◽  
Vol 51 (4) ◽  
pp. 1919-1930
Author(s):  
Masoumeh Akbarizadeh ◽  
Mehdi Alaeiyan ◽  
Raffaele Scapellato
Keyword(s):  
Automorphism Groups

scholarly journals Serre’s Property (FA) for automorphism groups of free products

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Naomi Andrew
Keyword(s):  
Automorphism Group ◽  
Free Product ◽  
Finite Groups ◽  
Automorphism Groups ◽  
Sufficient Conditions ◽  
Free Products ◽  
Cyclic Groups ◽  
Link Type ◽  
Open Case

AbstractWe provide some necessary and some sufficient conditions for the automorphism group of a free product of (freely indecomposable, not infinite cyclic) groups to have Property (FA). The additional sufficient conditions are all met by finite groups, and so this case is fully characterised. Therefore, this paper generalises the work of N. Leder [Serre’s Property FA for automorphism groups of free products, preprint (2018), https://arxiv.org/abs/1810.06287v1]. for finite cyclic groups, as well as resolving the open case of that paper.

scholarly journals On a Unique Ergodicity of Some Markov Processes

2011 ◽  
Vol 36 (4) ◽  
pp. 589-606 ◽  
Author(s):  
Rafał Kapica ◽  
Tomasz Szarek ◽  
Maciej Ślȩczka
Keyword(s):  
Markov Processes ◽  
Unique Ergodicity
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