  Let T denote Thompson's group of piecewise 2-adic linear homeomorphisms of
the circle. Ghys and Sergiescu showed that the rotation number of every element
of T is rational, but their proof is very indirect. We give here a short,
direct proof using train tracks, which generalizes to PL homeomorphism of the
circle with rational break points and derivatives which are powers of some
fixed integer, and also to certain flows on surfaces which we call
"Thompson-like". We also obtain an explicit upper bound on the smallest period
of a fixed point in terms of data which can be read off from the combinatorics
of the homeomorphism

Dynamical Systems;Group Theory