Fluctuations of spatial patterns as a measure of classical chaos

In problems where the temporal evolution of a nonlinear system cannot be followed, a method for studying the fluctuations of spatial patterns has been developed. That method is applied to well-known problems in deterministic chaos (the logistic map and the Lorenz model) to check its effectiveness in characterizing the dynamical behaviors. It is found that the indices ${\mu }_q$ are as useful as the Lyapunov exponents in providing a quantitative measure of chaos. When applied to the Ising system of finite size, it is shown how ${\mu }_q$ can be used to determine the critical temperature.