Chaos Lab

Discrete map · 2D · dim 2

Lozi map

Piecewise-linear variant of Hénon. The Lozi attractor is a verifiable strange attractor (Misiurewicz's theorem 1980), unlike Hénon's, which is still open at the rigorous level.

Lozi attractor at (a, b) = (1.7, 0.5). Piecewise-linear cousin of Hénon.

Equations

x_{n+1} = 1 − a · |x_n| + y_n
y_{n+1} = b · x_n

At a glance

Parametersa, b ∈ ℝ (classic: a = 1.7, b = 0.5)
Chaotic forbroad band
HistoryLozi (1978); rigorous strange attractor proof by Misiurewicz (1980).

Try it

Open the interactive playground at /tools/henon.

See also

Quick quiz

Test yourself on lozi

8 multiple-choice questions. Pick an answer for each, then submit to see explanations.

  1. Q1.Lozi (1978) replaces the quadratic in Hénon with which nonlinearity?

  2. Q2.A standard Lozi parameter set is:

  3. Q3.Lozi is interesting historically because it was the first 2D map with:

  4. Q4.Misiurewicz's rigorous Lozi-attractor result appeared in:

  5. Q5.Numerical Lyapunov exponent of Lozi at (1.7, 0.5) is:

  6. Q6.Compared to Hénon, Lozi has:

  7. Q7.Lozi map is dissipative when:

  8. Q8.Lozi is pedagogically valuable because:

0 of 8 answered