Tent

Systems / Maps / Geometric maps

The piecewise-linear tent map — exact, fully chaotic, conjugate to the binary shift.

discrete · map1 dimensionchaotic

return map · bifurcation diagram

Definition

\[ \begin{aligned} y_{0}' &= \mu \left(1 - 2 \left|{y_{0} - 0.5}\right|\right) \end{aligned} \]

Parameters

Symbol	Default	Role
mu	0.95	peak height (branch slope magnitude 2*mu)

Properties

Lyapunov spectrum

$+0.6419$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 1$

Divergence ∇·f

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

Equilibria

2 fixed points
0 stable · 2 unstable

Define it in TSDynamics

import tsdynamics as ts

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

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

Reference

Classical map; see e.g. Strogatz, Nonlinear Dynamics and Chaos

BibTeX

@misc{tent,
  title = {Tent system},
  note = {Classical map; see e.g. Strogatz, Nonlinear Dynamics and Chaos}
}