Chaos as Field

The modern theory of dynamical systems begins with a paradox. On the one hand, many systems of interest - physical, biological, social, and cognitive - are governed by precise and deterministic laws. Their evolution is described by equations that admit unique solutions for given initial conditions. On the other hand, these same systems often exhibit behavior that is irregular, non-periodic, andeffectively unpredictable over long time horizons. This tension between determinism and unpredictability is not an anomaly but a structural feature of a large class of systems now understood under the name of chaos.