Dynamics of the third order Lyness' difference equation
Dynamics of the third order Lyness' difference equation
This paper studies the iterates of the third order Lyness' recurrence $x_{k+3}=(a+x_{k+1}+x_{k+2})/x_k,$ with positive initial conditions, being $a$ also a positive parameter. It is known that for $a=1$ all the sequences generated by this recurrence are 8-periodic. We prove that for each $a\ne1$ there are infinitely many initial conditions giving …