# Advanced Topics - Demo 7

## Quadratic map above *a*_{c}: Chaos at Band Merging

It is interesting to compare the probability density at band merging with the analytically known probability at the "most chaotic" value of *a=4*

At band merging:

It is again useful to look at the 4th iterate of the map (enlarge the visited portion of the x-axis using the mouse):

and compare this with the behavior over the whole unit interval at *a=4*:

The histograms have essentially the same form (and then the first plot is made up of the 4 bands with the same distribution, but with different scales).

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Last modified Friday, February 4, 2000

Michael Cross