** Author: ** Jason D. Mireles-James

** Abstract:**This work describes a method for computing polynomial expansions of a one
parameter branch of stable or unstable manifolds associated with hyperbolic fixed points or
equilibria of a family of analytic dynamical systems. We develop a-posteriori theorems which
provide mathematically rigorous bounds on the truncation errors associated the polynomial
expansions. The hypotheses of these theorems are formulated in terms of certain inequalities
which are checked via a finite number of calculations on a digital computer. Exploiting the
analytic properties of the dynamical systems we are able to obtain mathematically rigorous
bounds on the jets of the manifolds, as well as on the derivatives of the manifolds with
respect to the parameter. A number of example computations are given.

"Preprint available here"