The dynamics of homeomorphisms of hereditarily decomposable chainable continua

Let M be a hereditarily decomposable chainable continuum and F be a homeomorphism of M. We show that the periods of the periodic orbits of F are powers of 2 and for each x ϵ R(F), either ω(x, F) is a periodic orbit of F or (ω(x, F), F) is semi-conjugate to the adding machine. Partially answering a problem of Marcy Barge we prove that homeomorphisms of Suslinean chainable continua have zero topological entropy. By the same idea homeomorphisms of Suslinean circle-like continua also have zero topological entropy.