Henon¶

Systems / Maps / Chaotic maps

The Hénon map — a 2-D quadratic map whose folded attractor is the canonical strange attractor of dissipative maps.

discrete · map2 dimensionschaotic

Definition¶

\[ \begin{aligned} x' &= - a x^{2} + y + 1.0 \\ y' &= b x \end{aligned} \]

Symbol	Default	Role
`a`	`1.4`	stretching
`b`	`0.3`	area contraction

State variables: x, y

Lyapunov spectrum

$+0.419,\; -1.623$
Sprott (2003), Chaos and Time-Series Analysis

Kaplan–Yorke dimension

$D_{KY} = 1.258$

Divergence ∇·f

n/a — discrete map — flow divergence undefined (per-step contraction is |det J|)

Equilibria

2 fixed points
0 stable · 2 unstable

import tsdynamics as ts

sys = ts.systems.Henon()
traj = sys.iterate(steps=10_000)

exps = sys.lyapunov_spectrum()
ts.kaplan_yorke_dimension(exps)

Hénon (1976), Commun. Math. Phys. 50, 69-77

BibTeX

@misc{henon,
  title = {Henon system},
  note = {Hénon (1976), Commun. Math. Phys. 50, 69-77}
}