Bifurcations and periods in chaos with HP50G

[Gil]

The solver solution of HP50G should be correct.

The bifurcation point "1.25“ gives 4 iterating points for a values = 1.25+epsilon, with epsilon tiny and ≠0, and not for a exactly =1.25.

Corresponding simplification with
X[n+3]=a-X[n+2]²
X[n+2]=a-X[n+1]²

And X[n+3]=X[n+1]

Then
'1.25-(1.25-X1^2)^2-X1' :
Roots: [ -.207106781187 .724744871392 1.20710678119 -1.72474487139 ]

And only 2 oscillation points:-0.207... and +1.207...