Gingerbreadman¶

Systems / Maps / Chaotic maps

A piecewise-linear map tiling the plane with quasiperiodic gingerbread-man cells.

discrete · map2 dimensionsquasiperiodic

Definition¶

\[ \begin{aligned} y_{0}' &= - y_{1} + \left|{y_{0}}\right| + 1 \\ y_{1}' &= y_{0} \end{aligned} \]

Properties¶

Lyapunov spectrum

$-2.781e-17,\; -6.477e-17$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 0$

Divergence ∇·f

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

Equilibria

1 fixed points
0 stable · 1 unstable

Define it in TSDynamics¶

import tsdynamics as ts

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

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

Reference¶

Devaney (1984), Physica D 10, 387-393

BibTeX

@misc{gingerbreadman,
  title = {Gingerbreadman system},
  note = {Devaney (1984), Physica D 10, 387-393}
}