Systematic renormalisation-group theory for non-Markovian dynamics in functional phase space

Formulate a systematic renormalisation-group framework for non-Markovian deterministic dynamics in functional phase space that captures how long-range temporal memory acts as a relevant operator and organizes universality classes of chaos.

Background

Feigenbaum universality in Markovian maps is explained by a finite-dimensional renormalisation-group fixed point. The present work demonstrates that long-range memory is a relevant perturbation that generates a new universality class, suggesting the need for an RG formalism acting on histories (functional degrees of freedom) rather than states.

A comprehensive RG treatment for non-Markovian dynamics—capable of predicting scaling exponents, fixed points, and stability in the presence of memory kernels—remains to be established.

References

Several open theoretical questions arise naturally. The role of long‑range memory in reshaping universality in higher‑dimensional systems and continuous‑time flows remains largely unexplored, as does the formulation of a systematic renormalisation‑group theory for non‑Markovian dynamics in functional phase space.

— Universality classes of chaos in non Markovian dynamics (2512.22445 - Vijayan, 27 Dec 2025) in Section: Implications and Outlook