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.