top
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.
Enhui Shi, and Suhua Wang. "The ping-pong game, geometric entropy and expansiveness for group actions on Peano continua having free dendrites." Fundamenta Mathematicae 203.1 (2009): 21-37. <http://eudml.org/doc/283153>.
@article{EnhuiShi2009, 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.}, author = {Enhui Shi, Suhua Wang}, journal = {Fundamenta Mathematicae}, keywords = {Peano continuum; expansiveness; group action; geometric entropy; ping-pong game; free dendrite}, language = {eng}, number = {1}, pages = {21-37}, title = {The ping-pong game, geometric entropy and expansiveness for group actions on Peano continua having free dendrites}, url = {http://eudml.org/doc/283153}, volume = {203}, year = {2009}, }
TY - JOUR AU - Enhui Shi AU - Suhua Wang TI - The ping-pong game, geometric entropy and expansiveness for group actions on Peano continua having free dendrites JO - Fundamenta Mathematicae PY - 2009 VL - 203 IS - 1 SP - 21 EP - 37 AB - 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. LA - eng KW - Peano continuum; expansiveness; group action; geometric entropy; ping-pong game; free dendrite UR - http://eudml.org/doc/283153 ER -