The ping-pong game, geometric entropy and expansiveness for group actions on Peano continua having free dendrites

Volume 203 / 2009

Enhui Shi, Suhua Wang 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.

Authors

  • Enhui ShiDepartment of Mathematics
    Suzhou University
    Suzhou 215006, P.R. China
    e-mail
    e-mail
  • Suhua WangDepartment of Mathematics
    Suzhou University
    Suzhou 215006, P.R. China
    e-mail

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