Some dynamical properties of mappings defined on Knaster continua

We present an arc-like continuum X and a mapping f :X→X with the following properties: The set of recurrent points of f is dense in X; f has no periodic points other than fixed points; and the topological entropy of f is positive. This example allows us to answer one question due to J.J. Charatonik and another question due to M. Barge.