A transitive homeomorphism on the Lelek fan

Let X be a continuum and let φ:X→X homeomorphism. To construct dynamical system (X,φ) with interesting properties, the often needs to have some complicated topological structure. In this paper, we are interested in one such property: transitivity. By now, various examples of continua been constructed way that is transitive. Mostly, they not path-connected, as pseudo-arc or pseudo-circle, locally connected (and every path-connected), Sierpiński carpet an example. present example (X,φ), where φ homeomorphism on path-connected but continuum. We transitive Lelek fan. As by-product, non-invertible map fan also constructed.