Bifurcation
Named by 4 essays across one field — each of them below, with the objects they name alongside it.
The road paved with doublings
Turn one dial slowly and watch what a map settles into. It settles on a point, then on two points, then four, then eight — faster and faster, and the doublings run out at a parameter that is finite.
A constant that does not care which map
The gaps between successive period doublings shrink by a factor. Measure that factor for the logistic map and you get 4.669. Measure it for a completely different map and you get 4.669, and nobody expected that.
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.
Two lobes and no cycle
Three equations, three variables, and a trajectory that never crosses itself, never repeats, and never leaves a region of zero volume. The set it settles onto is not a point, not a loop, and not a surface.
Named alongside it
The objects these essays reach for when they reach for this one.
Logistic mapAttractorChaosOrbitPeriod doublingSelf similaritySensitive dependenceAverageConvergenceDerivativeDissipationFeigenbaum constant