Two-Dimensional Constrained Chaos and Industrial Revolution Cycles with Mathemetical Appendices

Between the 1760s and 1980s, we have experienced at least three industrial revolutions. We explain such cycles as ergodic chaos and relate it to the average long-run interest rate and intellectual property protection. Because innovation dynamics is intrinsically multi-dimensional, we need newly to develop a structural characterization of multi-dimensional ergodic chaos suitable for an economic analysis. Introducing such a characterization for the two-dimensional case, we show that if the monopolistic use of a new invention lasts eight years, an industrial-revolution-like burst of new technologies recurs about every one hundred years, given empirically reasonable values of the determinants of a long-run interest rate