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Playing with the Hénon Map Starting with a Circle or a Square

​
options
the initial figure
F
0
circle
square
number of iterations
n
10
main control parameter
a
0.19
dissipation parameter
b
1
2Δ, the size of plot range
Δ
5
2r, the size of
F
0
r
1.191
notes
C
0
is the center of
F
0
C
n
is the
th
n
iterated image of
C
0
This Demonstration shows iterates of the dissipative Hénon map [1–4],
(
x
n+1
,
y
n+1
)=1+b
y
n
-a
2
x
n
,
x
n
, where
a
and
b
are real, acting on 500 equally spaced initial points
(
x
0
,
y
0
)
on a circle or a square. You can drag the crosshairs-shaped locator to change the position of
C
0
.
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