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

A Bayesian nonparametric approach to the approximation of the global stable manifold