This is lecture 22 in the series "Introduction to the Mathematics of Climate" offered at the University of Minnesota in 2014 with the support of MCRN and The Institute for Mathematics and its Applications.
This lecture treats the phenomenon of exponential growth in errors for chaotic systems, using Lyapunov multipliers and exponents. In summary, in chaotic systems,
- positive Lyapunov exponents are associated with unpredictability,
- errors propagate exponentially,
- orbits behave randomly, and
- simple deterministic systems can have random behavior.
University of North Carolina at Chapel Hill Mathematics