Orbit Diagram of the Hénon Map

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This Demonstration shows an orbit of the Hénon map with 10000 points. With the slider controls you can vary the initial conditions of the orbit and the values of the two parameters of the system. Click the diagram to select an area of the orbit and see it magnified in the small window. Additional slider controls vary the degree of magnification in the small window and precision in the calculation.

Contributed by: C. Pellicer-Lostao and R. Lopez-Ruiz (March 2011)
Based on a program by: Ed Pegg Jr
Open content licensed under CC BY-NC-SA


Snapshots


Details

The Hénon map is given by the equations , .

This system exhibits chaotic behavior when and .

For certain ranges of the values of the parameters and the initial conditions, the dynamics can also converge to periodic orbits.



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