Notes

Chapter 4: Systems Based on Numbers

Section 7: Iterated Maps and the Chaos Phenomenon


Lyapunov exponents

The number of new digits that are affected at each step by a small change in initial conditions gives the so-called Lyapunov exponent λ for the evolution. After t steps, the difference in size resulting from the change in initial conditions will be multiplied by approximately 2^(λ t)—at least until this difference is of order 1. (See page 950.)

From Stephen Wolfram: A New Kind of Science [citation]