General Overview — Motivation and high-level objectives
The aim of DynAMiCs is to address a series of central and fundamental algorithmic questions about trajectories of discrete dynamical systems, some of which have been open for decades.
Our motivation and outlook are in large part - but not exclusively - driven by the paradigm of automated verification in computer science. We are chiefly interested in decision and model-checking problems about the behavior of discrete linear dynamical systems and related formalisms, both of a dynamical (or temporal) and arithmetical nature.
Discrete dynamical systems have for many years been the object of intense study in different communities, according to whether they are viewed as geometric or symbolic objects. As noted in [1], "the field of symbolic dynamics has its origins in the coding of concrete (geometrical) dynamical systems" (a correspondence going back a full century! [2][3]), yet there has been comparatively little interaction between the two communities.
This research project assembles a team of three internationally leading PIs, coming from algorithmic verification and geometric dynamical systems (PI Ouaknine), symbolic dynamics (PI Berthé), and analytic number theory (PI Luca). This combination brings complementary and synergistic expertise, and places the team in a unique position to achieve major breakthroughs in longstanding fundamental problems in the area of discrete dynamical systems.