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 2λ t—at least until this difference is of order 1. (See page 950.)


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