<P> where t is the time and λ is the Lyapunov exponent . The rate of separation depends on the orientation of the initial separation vector, so a whole spectrum of Lyapunov exponents exist . The number of Lyapunov exponents is equal to the number of dimensions of the phase space, though it is common to just refer to the largest one . For example, the maximal Lyapunov exponent (MLE) is most often used because it determines the overall predictability of the system . A positive MLE is usually taken as an indication that the system is chaotic . </P> <P> Also, other properties relate to sensitivity of initial conditions, such as measure - theoretical mixing (as discussed in ergodic theory) and properties of a K - system . </P> <P> Topological mixing (or topological transitivity) means that the system evolves over time so that any given region or open set of its phase space eventually overlaps with any other given region . This mathematical concept of "mixing" corresponds to the standard intuition, and the mixing of colored dyes or fluids is an example of a chaotic system . </P> <P> Topological mixing is often omitted from popular accounts of chaos, which equate chaos with only sensitivity to initial conditions . However, sensitive dependence on initial conditions alone does not give chaos . For example, consider the simple dynamical system produced by repeatedly doubling an initial value . This system has sensitive dependence on initial conditions everywhere, since any pair of nearby points eventually becomes widely separated . However, this example has no topological mixing, and therefore has no chaos . Indeed, it has extremely simple behavior: all points except 0 tend to positive or negative infinity . </P>

Which of the following is not a basic principle proposed by the physical symbol system theory