Bifurcation of the ACT map

Bau-Sen Du, Ming-Chia Li, Mikhail Malkin

In this paper, we study the Arneodo-Coullet-Tresser map $F(x,y,z)=(ax-b(y-z),bx+a(y-z),cx-d{x}^k+ez)$ where $a,b,c,d,e$ are real with $bd\ne 0$ and $k>1$ is an integer. We obtai…