scholarly journals On enveloping semigroups of nilpotent group actions generated by unipotent affine transformations of the torus

2010 ◽  
Vol 201 (2) ◽  
pp. 133-153 ◽  
Author(s):  
Rafał Pikuła
Keyword(s):  
Nilpotent Group ◽  
Group Actions ◽  
Affine Transformations ◽  
Enveloping Semigroups

Enveloping semigroups of unipotent affine transformations of the torus

2010 ◽  
Vol 30 (5) ◽  
pp. 1543-1559 ◽  
Author(s):  
RAFAŁ PIKUŁA
Keyword(s):  
Nilpotent Group ◽  
Nilpotency Class ◽  
Affine Transformations ◽  
Dimensional Torus ◽  
Constant Vector ◽  
Finite Dimensional ◽  
Enveloping Semigroup ◽  
Lower Triangular ◽  
Enveloping Semigroups

AbstractWe provide a description of the enveloping semigroup of the affine unipotent transformation T:X→X of the form T(x)=Ax+α, where A is a lower triangular unipotent matrix, α is a constant vector, and X is a finite-dimensional torus. In particular, we show that in this case the enveloping semigroup is a nilpotent group whose nilpotency class is at most the dimension of the underlying torus.

scholarly journals Topological correspondence of multiple ergodic averages of nilpotent group actions

2019 ◽  
Vol 138 (2) ◽  
pp. 687-715 ◽  
Author(s):  
Wen Huang ◽  
Song Shao ◽  
Xiangdong Ye
Keyword(s):  
Nilpotent Group ◽  
Group Actions ◽  
Ergodic Averages

scholarly journals Sharp regularity for certain nilpotent group actions on the interval

2013 ◽  
Vol 359 (1-2) ◽  
pp. 101-152 ◽  
Author(s):  
Gonzalo Castro ◽  
Eduardo Jorquera ◽  
Andrés Navas
Keyword(s):  
Nilpotent Group ◽  
Group Actions

scholarly journals Fixed points of discrete nilpotent group actions on $S^2$

2002 ◽  
Vol 52 (4) ◽  
pp. 1075-1091 ◽  
Author(s):  
Suely Druck ◽  
Fuquan Fang ◽  
Sebastião Firmo
Keyword(s):  
Nilpotent Group ◽  
Fixed Points ◽  
Group Actions

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.

AUSLANDER–YORKE CHAOS FOR GROUP ACTIONS ON DENDRITES

2013 ◽  
Vol 23 (06) ◽  
pp. 1350097 ◽  
Author(s):  
SUHUA WANG ◽  
ENHUI SHI ◽  
YUJUN ZHU ◽  
BIN CHEN
Keyword(s):  
Nilpotent Group ◽  
Group Action ◽  
Group Actions ◽  
Finitely Generated ◽  
Sensitive Group

We show that each sensitive group action on a dendrite contains an Auslander–Yorke chaotic subsystem. By this conclusion, we prove that each sensitive group action on a dendrite must have positive geometric entropy when the acting group is finitely generated, and no dendrite admits a sensitive nilpotent group action.

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