11529, Taipei, Taiwan
Institute of Mathematics, Academia Sinica, Taipei
Du B., Li M., Malkin M. I.
Topological horseshoes for Arneodo–Coullet–Tresser maps
2006, vol. 11, no. 2, pp. 181-190
In this paper, we study the family of Arneodo–Coullet–Tresser maps $F(x,y,z)=(ax-b(y-z)$, $bx+a(y-z)$, $cx-dxk+e z)$ where $a$, $b$, $c$, $d$, $e$ are real parameters with $bd \ne 0$ and $k>1$ is an integer. We find regions of parameters near anti-integrable limits and near singularities for which there exist hyperbolic invariant sets such that the restriction of $F$ to these sets is conjugate to the full shift on two or three symbols.