Plateau Dynamics: Operational Detection of Persistent Low-Dynamical Regimes in Observation Space

This work introduces a new geometry in observation space, where persistent low-dynamical regimes form directly observable structures in time series data. A plateau is defined as a contiguous interval satisfying simultaneous constraints on bounded drift, bounded variation, and minimum persistence. This operational definition transforms qualitative notions of “stability” into a precise, reproducible object that can be detected directly from data using local statistics. The method operates in linear time (O(N)) and requires no phase-space reconstruction or model fitting, enabling real-time and streaming applications. Beyond detection, the framework provides insight into the structure of dynamical systems by revealing how stability emerges as temporally extended, geometrically constrained regimes (“plateau islands”). A cumulative stability metric, O(t), quantifies the buildup of sustained low-dynamical behavior over time, allowing comparison across regimes. Together, plateau detection and cumulative quantification establish a practical, model-free bridge between observable statistics and underlying dynamical organization, with applications across physical, biological, and artificial systems