 The second problem with the standard account is that there simply is no implication that finite uncertainties will exhibit an on-average growth rate characterized by any Lyapunov exponents, local or global. For example, the linearized dynamics used to derive global Lyapunov exponents presupposes infinitesimal uncertainties  (Appendix (A1)–(A5)).   But when uncertainties are finite, such dynamics do not apply and no valid conclusions can be drawn about the dynamics of finite uncertainties from the dynamics of infinitesimal uncertainties. Certainly infinitesimal uncertainties never become finite in finite time (barring super exponential growth). Even if infinitesimal uncertainties became finite after a finite time, that would presuppose the dynamics is unconfined, whereas the interesting features of nonlinear dynamics usually take place in subregions of state space. Presupposing an unconfined dynamics would be inconsistent with the features we are typically trying to capture. 