Orbit Diagram of the Hénon Map

initial conditions

x

0

0.5

y

0

0.2

parameters

α

1.4

β

0.3

additional controls

magnification

7

precision

22

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.

Details

The Hénon map is given by the equations

x

n+1

=α

2

x

n

+

y

n

+1

,

y

n+1

=β

x

n

.

This system exhibits chaotic behavior when

α∈[1.16,1.41]

and

β∈[0.2,0.3]

.

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

External Links

Hénon Map (Wolfram MathWorld)

Logistic Map (Wolfram MathWorld)

Orbit Diagram of the Logistic Map

Permanent Citation

C. Pellicer-Lostao, R. Lopez-Ruiz, Ed Pegg Jr

"Orbit Diagram of the Hénon Map"
http://demonstrations.wolfram.com/OrbitDiagramOfTheHenonMap/
Wolfram Demonstrations Project
Published: March 7, 2011