Observable Lyapunov Exponents for Globally Coupled Maps in the Mean-Field Limit
Speaker: Masood Ahmad
Abstract: Large coupled systems can exhibit microscopic chaos alongside stable macroscopic behaviour. We introduce observable Lyapunov exponents to quantify this distinction. For globally coupled maps, we show that these exponents are determined by the linearisation of the self-consistent transfer operator. Applying this result to weakly coupled uniformly expanding maps, we prove that macroscopic perturbations decay near a stationary mean-field state, despite microscopic chaos. Our findings provide a rigorous framework for distinguishing microscopic and macroscopic chaos.