scholarly journals Topological transitivity of solvable group actions on the line R

2009 ◽  
Vol 116 (2) ◽  
pp. 203-215 ◽  
Author(s):  
Suhua Wang ◽  
Enhui Shi ◽  
Lizhen Zhou ◽  
Grant Cairns
Keyword(s):  
Solvable Group ◽  
Group Actions ◽  
Topological Transitivity

scholarly journals Measure rigidity for solvable group actions in the space of lattices

2019 ◽  
Vol 189 (3) ◽  
pp. 421-428
Author(s):  
Manfred Einsiedler ◽  
Ronggang Shi
Keyword(s):  
Solvable Group ◽  
Group Actions ◽  
Measure Rigidity

scholarly journals Topological Transitivity and Mixing Notions for Group Actions

2007 ◽  
Vol 37 (2) ◽  
pp. 371-397 ◽  
Author(s):  
Grant Cairns ◽  
Alla Kolganova ◽  
Anthony Nielsen
Keyword(s):  
Group Actions ◽  
Topological Transitivity

TOPOLOGICAL TRANSITIVITY AND CHAOS OF GROUP ACTIONS ON DENDRITES

2009 ◽  
Vol 19 (12) ◽  
pp. 4165-4174 ◽  
Author(s):  
SUHUA WANG ◽  
ENHUI SHI ◽  
LIZHEN ZHOU ◽  
XUNLI SU
Keyword(s):  
Nilpotent Group ◽  
Group Action ◽  
Group Actions ◽  
Finitely Generated ◽  
Topological Transitivity ◽  
Ping Pong ◽  
Weakly Mixing

We show that each weakly mixing group action on a dendrite must have a ping-pong game, and has positive geometric entropy when the acting group is finitely generated. As a corollary, we prove that no nilpotent group action on a dendrite is weakly mixing. At last, we show that each dendrite admits no chaotic group actions.

Group actions and non-vanishing elements in solvable groups

2020 ◽  
Vol 23 (6) ◽  
pp. 1103-1109
Author(s):  
Thomas R. Wolf
Keyword(s):  
Solvable Group ◽  
Group Actions ◽  
Solvable Groups ◽  
Direct Sum ◽  
Irreducible Modules ◽  
Group A ◽  
Vanishing Elements

AbstractFor a solvable group, a theorem of Gaschutz shows that {F(G)/\Phi(G)} is a direct sum of irreducible G-modules and a faithful {G/F(G)}-module. If each of these irreducible modules is primitive, we show that every non-vanishing element of G lies in {F(G)}.

Li-York Chaos of Set-Valued Discrete Dynamical Systems Based on Semi-Group Actions

2013 ◽  
Vol 380-384 ◽  
pp. 1778-1782
Author(s):  
Yun Qian ◽  
Peng Guan
Keyword(s):  
Dynamical Systems ◽  
Periodic Point ◽  
Metric Space ◽  
Hausdorff Metric ◽  
Group Actions ◽  
Discrete Dynamical Systems ◽  
Semi Group ◽  
Topological Transitivity ◽  
Hausdorff Metric Space

t is well known that a semi-groups action on a space could appear chaos phenomenon, like Li-York chaos and so on. Li-York chaos has important relations with topological transitivity and periodic point. This study analyzed metric space and its dinduced Hausdorff metric space. Letis a semi-group. We make continuously act on space. We study topological transitivity and betweenand. Some important results are presented which show that if is topological transitivity and periodicity (which means Li-York chaos at the same time), then the action of semi-grouponis Li-York chaos.

Disjoint topological transitivity for weighted translations generated by group actions

2021 ◽  
Vol 71 (5) ◽  
pp. 1229-1240
Author(s):  
Chung-Chuan Chen ◽  
Seyyed Mohammad Tabatabaie ◽  
Ali Mohammadi
Keyword(s):  
Group Actions ◽  
Group Element ◽  
Necessary Condition ◽  
Compact Groups ◽  
Topological Transitivity ◽  
Locally Compact ◽  
Topological Mixing ◽  
Quotient Spaces ◽  
Sufficient And Necessary Condition

Abstract In this note, we give a sufficient and necessary condition for weighted translations, generated by group actions, to be disjoint topologically transitive in terms of the weights, the group element and the measure. The characterization of disjoint topological mixing is obtained as well. Moreover, we apply the results to the quotient spaces of locally compact groups and hypergroups.

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