Method for extracting arbitrarily large orbital equations of the Pincherle map

We report an algorithm to extract equations of motion for orbits of arbitrarily high periods generated by iteration of the Pincherle map, the operational kernel used in the so-called chaotic computers. The performance of the algorithm is illustrated explicitly by extracting expeditiously, among others, an orbit buried inside a polynomial cluster of equations with degree exceeding one billion, out of reach by ordinary brute-force factorization. Large polynomial clusters are responsible for the organization of the phase-space and knowledge of this organization requires decomposing such clusters. Keywords: Algebraic dynamics, Preperiodic points, Orbital decomposition, Chaotic computer