Pavel Popovich

Contraction versus Recurrence: An Exponential Separation in Observation-Based Prediction of Deterministic Dynamics

Given a scalar observable of an ergodic dynamical system with a low-dimensional attractor, two families of methods reconstruct and predict the underlying state: recurrence-based methods (the method of analogues and its descendants), which wait for the trajectory to return to an $\varepsilon$-neighborhood of a previousl...