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

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

On isolated fixed points of group actions on poincaré complexes

Mathematika ◽  
1974 ◽  
Vol 21 (1) ◽  
pp. 114-115 ◽  
Author(s):  
J. P. E. Hodgson
Keyword(s):  
Fixed Points ◽  
Group Actions

scholarly journals Global fixed points for nilpotent actions on the torus

2019 ◽  
Vol 40 (12) ◽  
pp. 3339-3367
Author(s):  
S. FIRMO ◽  
J. RIBÓN
Keyword(s):  
Fixed Point ◽  
Probability Measure ◽  
Nilpotent Group ◽  
Fixed Points ◽  
Nilpotent Groups ◽  
Rotation Vector

An isotopic to the identity map of the 2-torus, that has zero rotation vector with respect to an invariant ergodic probability measure, has a fixed point by a theorem of Franks. We give a version of this result for nilpotent subgroups of isotopic to the identity diffeomorphisms of the 2-torus. In such a context we guarantee the existence of global fixed points for nilpotent groups of irrotational diffeomorphisms. In particular, we show that the derived group of a nilpotent group of isotopic to the identity diffeomorphisms of the 2-torus has a global fixed point.

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