It is shown that each expansive group action on a Peano continuum having a free dendrite must have a ping-pong game, and has positive geometric entropy when the acting group is finitely generated. As a corollary, it is shown that each Peano continuum having a free dendrite admits no expansive nilpotent group actions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-1-2,
author = {Enhui Shi and Suhua Wang},
title = {The ping-pong game, geometric entropy and expansiveness for group actions on Peano continua having free dendrites},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {21-37},
zbl = {1169.54018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-1-2}
}
Enhui Shi; Suhua Wang. The ping-pong game, geometric entropy and expansiveness for group actions on Peano continua having free dendrites. Fundamenta Mathematicae, Tome 205 (2009) pp. 21-37. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-1-2/