Bifurcation of the ACT map
| dc.creator | Du, Bau-Sen | |
| dc.creator | Li, Ming-Chia | |
| dc.creator | Malkin, Mikhail | |
| dc.date | 2007-09-07 | |
| dc.date | 2007-09-09 | |
| dc.date.accessioned | 2026-07-07T08:28:13Z | |
| dc.date.available | 2026-07-07T08:28:13Z | |
| dc.description | In this paper, we study the Arneodo-Coullet-Tresser map $ F(x,y,z)=(ax-b(y-z), bx+a(y-z), cx-dx^k+e z)$ where $a,b,c,d,e$ are real with $bd\neq 0$ and $k>1$ is an integer. We obtain stability regions for fixed points of $F$ and symmetric period-2 points while $c$ and $e$ vary as parameters. Varying $a$ and $e$ as parameters, we show that there is a hyperbolic invariant set on which $F$ is conjugate to the full shift on two or three symbols. We also show that chaotic behaviors of $F$ while $c$ and $d$ vary as parameters and $F$ is near an anti-integrable limit. Some numerical results indicates $F$ has Hopf bifurcation, strange attractors, and nested structure of invariant tori. | |
| dc.identifier | https://arxiv.org/abs/0709.1116 | |
| dc.identifier | http://arxiv.org/abs/0709.1116 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137538 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37G10, 37C25, 37C70, 37E99 | |
| dc.title | Bifurcation of the ACT map | |
| dc.type | text |