amath

## Periodic Behavior of the Hénon Map

Say, we fix \beta at 0.4.
We see fixed points for \alpha=0.2:

We see a period-two sink for \alpha=0.5:

We see a period-four sink for \alpha=0.9:

Since some orbits are unbounded and go off to infinity, the choice of the seed is important in visualizing the behavior of the Hénon map.
Henon_map.m takes (0.1,0) as its seed.
The bifurcation diagram plotted below illustrates the period-doubling route to the chaotic attractor.

The MATLAB m-file, bifur_Henonmap.m creates the bifurcation diagram with the \alpha and \beta values as input.