a: 1.40
b: 0.30
d_H ≈ 1.261
b: 0.30
d_H ≈ 1.261
Hénon map (1976):
x_{n+1} = 1 − ax_n² + y_n
y_{n+1} = bx_n
At a=1.4, b=0.3: strange attractor with Hausdorff dimension ≈ 1.261.
Jacobian = −b everywhere → area contracts by |b| per step. Attractor is a fractal Cantor set in the transverse direction.
x_{n+1} = 1 − ax_n² + y_n
y_{n+1} = bx_n
At a=1.4, b=0.3: strange attractor with Hausdorff dimension ≈ 1.261.
Jacobian = −b everywhere → area contracts by |b| per step. Attractor is a fractal Cantor set in the transverse direction.