The ping-pong game, geometric entropy and expansiveness for group actions on Peano continua having free dendrites
Volume 203 / 2009
Fundamenta Mathematicae 203 (2009), 21-37
MSC: Primary 54H20; Secondary 37B05.
DOI: 10.4064/fm203-1-2
Abstract
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.
