Year: 2026
Type: preprint
Abstract: We study two notions of pluripotency for dynamical systems. Strong pluripotency refers to the possibility of reprogramming, by arbitrarily small perturbations, the forward orbits of points in a set of positive Riemannian volume so that they track a prescribed orbit in a uniform time-averaged sense. In contrast, pluripotency, also called ``statistical pluripotency" in this paper, requires only asymptotic agreement of empirical measures. Strong pluripotency implies statistical pluripotency, but the converse need not hold. For $C^r$ transitive Anosov diffeomorphisms, $r\ge2$, we prove that strong pluripotency fails for every nonempty reference set. On the other hand, statistical pluripotency holds for a nonempty reference set if and only if it is contained in the basin of the unique SRB measure. This basin is invariant and has full Riemannian volume, but contains no periodic points. These results reveal a sharp distinction between the two notions even within uniformly hyperbolic dynamics.
Source: arXiv (Cornell University)
Authors: Kiriki, Shin, Li, Xiaolong, Yamamoto, Kodai
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2188775277, G4394197504
OpenAlex ID: W7223303145