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 $\leq 2$ .

Mean Proximality, Mean Sensitivity and Mean Li–Yorke Chaos for Amenable Group Actions

2018 ◽  
Vol 28 (02) ◽  
pp. 1850028 ◽  
Author(s):  
Kesong Yan ◽  
Fanping Zeng
Keyword(s):  
Abelian Group ◽  
Periodic Point ◽  
Group Action ◽  
Amenable Group ◽  
Group Actions ◽  
Amenable Groups ◽  
Transitive Point ◽  
Infinite Abelian Group ◽  
Mean Sensitivity

We consider mean proximality and mean Li–Yorke chaos for [Formula: see text]-systems, where [Formula: see text] is a countable discrete infinite amenable group. We prove that if a countable discrete infinite abelian group action is mean sensitive and there is a mean proximal pair consisting of a transitive point and a periodic point, then it is mean Li–Yorke chaotic. Moreover, we give some characterizations of mean proximal systems for general countable discrete infinite amenable groups.

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.

DYNAMICS OF MONOTONE GRAPH, DENDRITE AND DENDROID MAPS

2011 ◽  
Vol 21 (11) ◽  
pp. 3205-3215 ◽  
Author(s):  
ISSAM NAGHMOUCHI
Keyword(s):  
Periodic Point ◽  
Periodic Points ◽  
Nonempty Interior ◽  
Limit Set ◽  
Limit Sets ◽  
Dendrite Map ◽  
Graph Map ◽  
Monotone Graph

We show that, for monotone graph map f, all the ω-limit sets are finite whenever f has periodic point and for monotone dendrite map, any infinite ω-limit set does not contain periodic points. As a consequence, monotone graph and dendrite maps have no Li–Yorke pairs. However, we built a homeomorphism on a dendroid with a scrambled set having nonempty interior.

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