  We study the dynamics of complex polynomials. We obtain results on Poincare
return maps defined on certain neighborhoods of a point with bounded orbit
under a polynomial. We introduce a generalization of the Yoccoz tau-function,
the Yoccoz return function, which codes the returns of a critical point with
bounded orbit of any complex polynomial with a disconnect Julia set. We give
necessary conditions on Yoccoz return functions, which allow for the recursive
definition of an abstract tau-function. These conditions are also sufficient
for polynomials that have a disconnected Julia set and exactly one critical
point with bounded orbit.
