Lyapunov exponent
Named by 5 essays across one field — each of them below, with the objects they name alongside it.
How fast two orbits part
The word "sensitive" is an adjective. Averaging the logarithm of one derivative along an orbit turns it into a number — one that says how many steps of prediction the map allows, and whose sign says whether it allows any.
The same map in different coordinates
The tent map and the logistic map at four look nothing alike and are the same map, carried onto each other by a change of variable. Everything either one does the other does, and the change of variable is a sine squared.
The obstacle that makes a table chaotic
Put one round post in the middle of a square table and every trace of order goes. Two paths that start a hundred-thousandth of a degree apart end up on opposite sides of the table, and the reason is that a wall curving outwards multiplies a gap where a flat one only adds to it.
A closer start buys only time
Two trajectories from almost the same place separate exponentially, and the rate does not depend on how close they began. Halving the initial error buys one fixed interval of extra agreement, and no amount of precision buys more than a fixed number of those.
A dimension from the stretching rates
An attractor has no construction rule, so its dimension has to be counted — that was the rung below's argument for defining dimension by counting at all. Kaplan and Yorke's formula computes it instead, from two numbers that describe the map and never look at the set.
Named alongside it
The objects these essays reach for when they reach for this one.
Sensitive dependenceChaosIterationLogarithmLogistic mapAttractorAverageBifurcationBilliardsBox dimensionChange of variableConjugacy