Amenable group actions and the Novikov conjecture

2000 ◽  
Vol 2000 (519) ◽  
Author(s):  
Nigel Higson ◽  
John Roe
Keyword(s):  
Amenable Group ◽  
Group Actions ◽  
Novikov Conjecture

scholarly journals The Katok's entropy formula for amenable group actions

2018 ◽  
Vol 38 (9) ◽  
pp. 4467-4482
Author(s):  
Xiaojun Huang ◽  
◽  
Jinsong Liu ◽  
Changrong Zhu ◽  
◽  
...  
Keyword(s):  
Amenable Group ◽  
Group Actions ◽  
Entropy Formula

scholarly journals Zero-dimensional extensions of amenable group actions

2021 ◽  
Vol 256 (2) ◽  
pp. 121-145
Author(s):  
Dawid Huczek
Keyword(s):  
Amenable Group ◽  
Group Actions

Relative Entropy and Mean Li–Yorke Chaos for Biorderable Amenable Group Actions

2020 ◽  
Vol 30 (02) ◽  
pp. 2050032
Author(s):  
Kesong Yan ◽  
Fanping Zeng
Keyword(s):  
Topological Entropy ◽  
Relative Entropy ◽  
Amenable Group ◽  
Group Actions

We consider the relative entropy and mean Li–Yorke chaos for [Formula: see text]-systems, where [Formula: see text] is a countable discrete infinite biorderable amenable group. We prove that positive relative topological entropy implies a multivariant version of mean Li–Yorke chaos on fibers for a [Formula: see text]-system.

scholarly journals Periodic points for amenable group actions on uniquely arcwise connected continua

2020 ◽  
pp. 1-12
Author(s):  
ENHUI SHI ◽  
XIANGDONG YE
Keyword(s):  
Periodic Point ◽  
Amenable Group ◽  
Group Actions ◽  
Periodic Points ◽  
Arcwise Connected

Abstract We show that any action of a countable amenable group on a uniquely arcwise connected continuum has a periodic point of order $\leq 2$ .

scholarly journals Sofic entropy and amenable groups

2011 ◽  
Vol 32 (2) ◽  
pp. 427-466 ◽  
Author(s):  
LEWIS BOWEN
Keyword(s):  
Group Action ◽  
Amenable Group ◽  
Group Actions ◽  
Amenable Groups ◽  
Orbit Equivalent ◽  
Sofic Entropy ◽  
Classical Entropy

AbstractIn previous work, the author introduced a measure-conjugacy invariant for sofic group actions called sofic entropy. Here, it is proven that the sofic entropy of an amenable group action equals its classical entropy. The proof uses a new measure-conjugacy invariant called upper-sofic entropy and a theorem of Rudolph and Weiss for the entropy of orbit-equivalent actions relative to the orbit changeσ-algebra.

scholarly journals Discrete spectrum for amenable group actions

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Tao Yu ◽  
Guohua Zhang ◽  
Ruifeng Zhang
Keyword(s):  
Invariant Measure ◽  
Discrete Spectrum ◽  
Invariant Measures ◽  
Hamming Distance ◽  
Amenable Group ◽  
Group Actions ◽  
The Mean

<p style='text-indent:20px;'>In this paper, we study discrete spectrum of invariant measures for countable discrete amenable group actions.</p><p style='text-indent:20px;'>We show that an invariant measure has discrete spectrum if and only if it has bounded measure complexity. We also prove that, discrete spectrum can be characterized via measure-theoretic complexity using names of a partition and the Hamming distance, and it turns out to be equivalent to both mean equicontinuity and equicontinuity in the mean.</p>

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