Feigenbaum constant
Published:
The Feigenbaum constants are two mathematical constants which both express ratios in a bifurcation diagram for a non-linear map. They are named after the mathematician Mitchell Feigenbaum. These constants are universal, so they applied to many different systems, independently of their nature.
Limiting ratio $\delta$:
\[{\displaystyle \delta =\lim _{n\rightarrow \infty }{\dfrac {a_{n-1}-a_{n-2}}{a_{n}-a_{n-1}}}=4.669\,201\,609\,\cdots }\]where $a_n$ are discrete values of a at the nth period doubling.
See also
Material
- Moriarty, Philip; Bowley, Roger (2009). δ - Feigenbaum Constant. Sixty Symbols. Brady Haran for the University of Nottingham.
Papers
- Briggs, Keith (1997). feigenbaum scaling in discrete dynamical systems. Annals of Mathematics (Thesis).