What are the Feigenbaum constants?

The Feigenbaum constants are two mathematical constants that express ratios in a bifurcation diagram for a non-linear map. Discovered by American mathematical physicist Mitchell J. Feigenbaum, these constants play a significant role in bifurcation theory and the study of chaos theory. Like other mathematical constants, they have fixed values defined unambiguously.

What we know

• The Feigenbaum constants delta and alpha are two mathematical constants expressing ratios in a bifurcation diagram for a non-linear map. [2]
• The constants are named after the physicist Mitchell J. Feigenbaum. [2]
• Mitchell J. Feigenbaum's pioneering studies in chaos theory led to the discovery of the constants. [3]
• Mathematical constants have values fixed by unambiguous definitions and are frequently referred to by special symbols or names. [5]

Where to go next

• whoWho was Mitchell Feigenbaum?
• how it workedHow does the logistic map generate chaos?
• the bigger pictureWhat is bifurcation theory?
• compared withWhat are other notable mathematical constants?
• how we knowHow did Edward Lorenz use the logistic map in climate systems?
• an unexpected connectionHow does population biology connect to chaos theory?The logistic map, which relates to the study of the Feigenbaum constants, was popularized by biologist Robert May as a discrete-time demographic model.

Sources

• [1]Feigenbaum constants (Wikidata Q673184) · CC0 1.0
• [2]Feigenbaum constants · CC BY-SA 4.0
• [3]Mitchell Feigenbaum · CC BY-SA 4.0
• [4]Logistic map · CC BY-SA 4.0
• [5]Mathematical constant · CC BY-SA 4.0