Mira's Equation has the form:
xn+1 = 2xn /(a2- xn2 ) - xn-1 ,
This equation has an equilibrium point p = (a2+ 1)1/2 .
This equation possesses an invariant
I(xn , xn-1 ) = xn2 xn-1 2 - a2( xn2 + xn-1 2 ) + 2 xn xn-1 .
Shown below is the surface of the invariant for the specific
value a = 2.
Here is the
animated graph
of invariant for the specific value a
= 2.
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