  We propose a Bayesian nonparametric model based on Markov Chain Monte Carlo
(MCMC) methods for unveiling the structure of the invariant global stable
manifold from observed time-series data. The underlying unknown dynamical
process is possibly contaminated by additive noise. We introduce the Stable
Manifold Geometric Stick Breaking Reconstruction (SM-GSBR) model with which we
reconstruct the unknown dynamic equations and in parallel we estimate the
global structure of the perturbed stable manifold. Our method works for
noninvertible maps without modifications. The stable manifold estimation
procedure is demonstrated specifically in the case of polynomial maps.
Simulations based on synthetic time series are presented.
