Windows for the quadratic map xn+1 = C - xn2 for periods up to 25

By

Madhura Joglekar

The link below is to a text file that has the 'window' data for all of the 1,402,957 primary periodic windows of periods not exceeding 25, lying in [Codd, 2], for the quadratic map xn+1 = C - xn2,
where Codd which is approximately 1.543689 denotes the largest parameter value before which there are no periodic windows of odd periods, other than the period-1 window.

The 4 columns of the matrix are as follows:


First column:         period of window
Second column:    saddle-node bifurcation value of window
Third column:       interior-crisis value of window
Fourth column:     C-width of window, that is, the difference between columns 2 and 3


I used tolerance values of 10-34 or smaller when computing window C-widths.

 

Rather than open the file below in a browser, I recommend that you first save the link and then open it with an appropriate program. Its size is about 140MB.


windows.txt